🚩 Report
Write an equation for the sentence: Four times a number less 10 is equal to 16.
A
4x - 10 = 16
B
4(x - 10) = 16
C
10 - 4x = 16
D
4x + 10 = 16
Explanation
Four times x is 4x, and 10 less gives 4x - 10.
🚩 Report
Etu has read 12 of the 32 chapters in his assigned book. He plans to finish the book by reading c chapters each day for 8 days. Which equation best represents the situation?
A
12 - 8c = 32
B
12 + c/8 = 32
C
12 + 8c = 32
D
12 - c/8 = 32
Explanation
The 12 chapters already read plus 8 days of c chapters per day equals 32.
🚩 Report
MOTORS: The horsepower H of a motor is the product of motor speed M and torque T divided by 5252. Translate the sentence into a formula.
A
H = M/(5252T)
B
H = MT/5252
C
H = 5252/(MT)
D
H = 5252M/T
Explanation
The product MT is divided by 5252, so H = MT/5252.
🚩 Report
Write a sentence for the equation 6z - 15 = 45.
A
Six times a number z, minus fifteen equals forty-five.
B
Six times the quantity of a number z minus fifteen equals forty-five.
C
Six times the difference of a number z and fifteen equals forty-five.
D
Six plus z minus fifteen equals forty-five.
Explanation
The equation first multiplies z by 6 and then subtracts 15.
🚩 Report
Write a sentence for the equation (y + 3)2 = 25.
A
y plus 3 squared is 25.
B
y squared plus 3 is 25.
C
The quantity y plus 3 squared is 25.
D
y plus 3 is 25.
Explanation
Parentheses show that the entire quantity y + 3 is squared.
🚩 Report
Select all statements that represent 7(p + 23) = 102. A: Seven times the sum of p and twenty-three is the same as one hundred two. B: Seven times p plus twenty-three equals one hundred two. C: Seven times the quantity p plus twenty-three equals one hundred two. D: The quantity seven times p plus twenty-three is the same as one hundred two. E: Seven times the sum of p and twenty-three is one hundred two.
A
A, C, and E
B
A, B, and E
C
B, C, and D
D
C, D, and E
Explanation
Statements A, C, and E all apply the factor 7 to the entire quantity p + 23.
🚩 Report
The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c. Which formula represents this statement?
A
P = a + b + c
B
P = a × b × c
C
P = a + b - c
D
P = (a + b + c)/2
Explanation
A triangle perimeter is the sum of its three side lengths.
🚩 Report
Write a sentence for the equation 4m = 52.
A
Four plus a number m equals fifty-two.
B
Four times a number m equals fifty-two.
C
A number m divided by four is fifty-two.
D
Four minus a number m equals fifty-two.
Explanation
The expression 4m means four times m.
🚩 Report
What is the verbal sentence for the equation 7(p + 23) = 102?
A
Seven times p plus twenty-three equals one hundred two.
B
Seven times the sum of p and twenty-three equals one hundred two.
C
The sum of seven and p multiplied by twenty-three is one hundred two.
D
Seven divided by the sum of p and twenty-three equals one hundred two.
Explanation
Parentheses make p + 23 a sum that is multiplied by 7.
🚩 Report
Write a sentence for the equation r2 - 15 = t + 19.
A
A number r squared minus fifteen equals a number t plus nineteen.
B
Two times r minus fifteen equals t plus nineteen.
C
The square root of r minus fifteen equals t plus nineteen.
D
r minus fifteen squared equals t plus nineteen.
Explanation
The exponent 2 applies to r, followed by subtracting 15.
🚩 Report
Solve 2/3 + w = 1 1/2. State which property of equality you used.
A
w = 5/6; Subtraction Property of Equality
B
w = 5/6; Addition Property of Equality
C
w = 13/6; Addition Property of Equality
D
w = 13/6; Subtraction Property of Equality
Explanation
Subtract 2/3 from both sides: w = 3/2 - 2/3 = 5/6.
🚩 Report
Solve the equation a + 26 = 35.
A
a = 61
B
a = 9
C
a = 11
D
a = 59
Explanation
Subtract 26 from both sides to get a = 9.
🚩 Report
On average, a male bulldog weighs 15 pounds less than a male golden retriever. If the average male bulldog weighs 50 pounds, write and solve an equation for the average weight w of a male golden retriever.
A
50 = w - 15; 65 pounds
B
50 = w + 15; 35 pounds
C
50 = w - 15; 35 pounds
D
50 = 15 - w; 65 pounds
Explanation
A bulldog is 15 pounds lighter, so 50 = w - 15 and w = 65.
🚩 Report
Solve the equation 6y = 54.
A
y = 6
B
y = 9
C
y = 12
D
y = 48
Explanation
Divide both sides by 6 to get y = 9.
🚩 Report
Solve the equation v - 9 = 14.
A
v = 5
B
v = 23
C
v = -5
D
v = 126
Explanation
Add 9 to both sides to get v = 23.
🚩 Report
Solve the equation 44 = t - 72.
A
t = -28
B
t = 28
C
t = 116
D
t = -116
Explanation
Add 72 to both sides: t = 44 + 72 = 116.
🚩 Report
Solve the equation -61 = d + (-18).
A
d = -79
B
d = 43
C
d = -43
D
d = 79
Explanation
Add 18 to both sides: d = -61 + 18 = -43.
🚩 Report
Solve the equation 18 + z = 40.
A
z = 58
B
z = -22
C
z = 22
D
z = 720
Explanation
Subtract 18 from both sides to get z = 22.
🚩 Report
Solve the equation -4a = 48.
A
a = 12
B
a = 52
C
a = -12
D
a = -192
Explanation
Divide both sides by -4 to get a = -12.
🚩 Report
Write an equation for the sentence and solve it: Six times a number is 132. Let n be the number.
A
6 + n = 132; n = 126
B
6n = 132; n = 22
C
n/6 = 132; n = 792
D
6n = 132; n = 792
Explanation
Six times n is 6n, and 132 divided by 6 is 22.
🚩 Report
Write an equation for the sentence and solve it: Two thirds equals negative eight times a number. Let n be the number.
A
2/3 = -8n; n = -1/12
B
2/3 = -8n; n = -3/16
C
(2/3)n = -8; n = -12
D
2/3 = -8n; n = 1/12
Explanation
Divide 2/3 by -8 to get n = -1/12.
🚩 Report
Solve the equation 3m + 4 = -11.
A
m = -5
B
m = 5
C
m = -7/3
D
m = -21
Explanation
Subtract 4 and divide by 3: m = -15/3 = -5.
🚩 Report
Solve the equation 8 = (x - 5)/7.
A
x = 51
B
x = 61
C
x = 21
D
x = 9
Explanation
Multiply by 7 to get 56 = x - 5, then add 5: x = 61.
🚩 Report
A sporting goods store sold 2/3 of its basketballs, but 8 were returned. Now the store has 38 basketballs. How many were there originally? Let b be the original number.
A
(2/3)b + 8 = 38; 45
B
(2/3)b - 8 = 38; 69
C
(1/3)b + 8 = 38; 90
D
(2/3)b + 8 = 38; 138
Explanation
After selling 2/3, the store has 1/3 of b left. Thus (1/3)b + 8 = 38 and b = 90. The source PDF incorrectly prints 2/3 in the intended correct choice, so that fraction is corrected here.
🚩 Report
Solve 2 - ax = -8 for x. Assume a ≠ 0.
A
x = -10/a
B
x = -6/a
C
x = 6/a
D
x = 10/a
Explanation
Subtract 2 to get -ax = -10, then divide by -a: x = 10/a.
🚩 Report
Use properties of equality to solve 3t + 7 = -8. Check your solution.
A
t = 5
B
t = -5
C
t = -1/3
D
t = -3
Explanation
Subtract 7 and divide by 3: t = -15/3 = -5.
🚩 Report
Use properties of equality to solve 8 = 16 + 8n. Check your solution.
A
n = 3
B
n = -3
C
n = 1
D
n = -1
Explanation
Subtract 16 to get -8 = 8n, so n = -1.
🚩 Report
Use properties of equality to solve -34 = 6m - 4. Check your solution.
A
m = -5
B
m = 5
C
m = -19/3
D
m = -6
Explanation
Add 4 to get -30 = 6m, so m = -5.
🚩 Report
Use properties of equality to solve 9x + 27 = -72. Check your solution.
A
x = -11
B
x = 11
C
x = -5
D
x = -9
Explanation
Subtract 27 and divide by 9: x = -99/9 = -11.
🚩 Report
Use properties of equality to solve f/(-7) - 8 = 2. Check your solution.
A
f = -70
B
f = 70
C
f = -14
D
f = 14
Explanation
Add 8 to get f/(-7) = 10, so f = -70.
🚩 Report
Use properties of equality to solve 1 + r/9 = 4. Check your solution.
A
r = 45
B
r = 27
C
r = -27
D
r = 3
Explanation
Subtract 1 to get r/9 = 3, so r = 27.
🚩 Report
Use properties of equality to solve k/3 + 4 = -16. Check your solution.
A
k = -36
B
k = 60
C
k = -60
D
k = -12
Explanation
Subtract 4 to get k/3 = -20, so k = -60.
🚩 Report
Use properties of equality to solve (n - 2)/7 = 2. Check your solution.
A
n = 12
B
n = 18
C
n = 14
D
n = 16
Explanation
Multiply by 7 and add 2: n - 2 = 14, so n = 16.
🚩 Report
Use properties of equality to solve 14 = (6 + z)/(-2). Check your solution.
A
z = -34
B
z = -22
C
z = 34
D
z = -40
Explanation
Multiply by -2: -28 = 6 + z, so z = -34.
🚩 Report
Use properties of equality to solve -11 = (a - 5)/6. Check your solution.
A
a = -61
B
a = -71
C
a = 51
D
a = -51
Explanation
Multiply by 6: -66 = a - 5, so a = -61.
🚩 Report
Use properties of equality to solve (22 - w)/3 = -7. Check your solution.
A
w = 43
B
w = -43
C
w = 1
D
w = 5
Explanation
Multiply by 3: 22 - w = -21, so -w = -43 and w = 43.
🚩 Report
Solve the equation 5 + 7a = 4a - 13.
A
a = -6
B
a = 6
C
a = -2
D
a = -8/3
Explanation
Subtract 4a and 5: 3a = -18, so a = -6.
🚩 Report
BASKETBALL: Last season Nolan scored 750 points in 30 games and Victor scored 782 points in 34 games. Assume they play every game this season and score at the same constant rates as last season. After how many games p will they have the same number of career points?
A
25p + 750 = 23p + 782; 16 games
B
30p + 750 = 34p + 782; 8 games
C
25p + 782 = 23p + 750; 10 games
D
750p + 30 = 782p + 34; 12 games
Explanation
Their rates are 25 and 23 points per game. Solving 25p + 750 = 23p + 782 gives p = 16.
🚩 Report
Solve the equation 7(n - 2) + 8 = 3(n - 4) - 2.
A
n = 4
B
n = 2
C
n = -3/2
D
n = -2
Explanation
Expand to 7n - 6 = 3n - 14, so 4n = -8 and n = -2.
🚩 Report
Solve the equation 5y = (12y + 16)/4.
A
y = 4
B
y = 2
C
y = -2
D
y = 8
Explanation
The right side is 3y + 4. Thus 5y = 3y + 4 and y = 2.
🚩 Report
GEOMETRY: A rectangle has width x cm and height 10 cm. A second rectangle has length (x + 3) cm and height 6 cm. Find x so the rectangles have the same area.
A
x = 9/2 (or 4.5)
B
x = 3
C
x = 9/4 (or 2.25)
D
x = 6
Explanation
Set 10x = 6(x + 3). Then 4x = 18, so x = 9/2.
🚩 Report
Solve the equation 6(y - 5) = 2(10 + 3y).
A
y = 5
B
y = -5
C
Infinitely many solutions (Identity)
D
No solution
Explanation
Expansion gives 6y - 30 = 20 + 6y, which reduces to -30 = 20, so there is no solution.
🚩 Report
Solve 3(2b - 1) - 7 = 6b - 10 and state whether it has one solution, no solution, or is an identity.
A
One solution: b = 0
B
No solution
C
Identity (Infinitely many solutions)
D
One solution: b = 1
Explanation
Both sides simplify to 6b - 10, so the equation is true for every b.
🚩 Report
Solve the equation 7c + 12 = -4c + 78.
A
c = 6
B
c = -6
C
c = 8
D
c = -8
Explanation
Add 4c and subtract 12: 11c = 66, so c = 6.
🚩 Report
Solve the equation 2m - 13 = -8m + 27.
A
m = -4
B
m = 2
C
m = -2
D
m = 4
Explanation
Add 8m and 13: 10m = 40, so m = 4.
🚩 Report
Solve the equation 9x - 4 = 2x + 3.
A
x = 1
B
x = -1
C
x = 7/11
D
x = -7/11
Explanation
Subtract 2x and add 4: 7x = 7, so x = 1.
🚩 Report
A triangle has base 8 and height x + 4. A rectangle has length x + 6 and width 3. Find x so the figures have the same area.
A
x = 1
B
x = 2
C
x = 3
D
x = 4
Explanation
Set (1/2)(8)(x + 4) = 3(x + 6). This gives 4x + 16 = 3x + 18, so x = 2.
🚩 Report
Solve -6y - 3 = 3 - 6y and state whether it has one solution, no solution, or is an identity.
A
One solution: y = 0
B
Identity (Infinitely many solutions)
C
No solution
D
One solution: y = -1
Explanation
Canceling -6y from both sides gives the false statement -3 = 3, so there is no solution.
🚩 Report
Solve (1/2)(x + 6) = (1/2)x - 9 and state whether it has one solution, no solution, or is an identity.
A
One solution: x = 0
B
Identity
C
No solution
D
One solution: x = -12
Explanation
The left side is x/2 + 3. Canceling x/2 gives 3 = -9, so there is no solution.
🚩 Report
Solve the equation 2x = 2(x - 3).
A
One solution: x = 3
B
Identity (Infinitely many solutions)
C
No solution
D
One solution: x = 0
Explanation
The right side is 2x - 6. Subtracting 2x gives 0 = -6, so there is no solution.
🚩 Report
Graph the solution set of |2t - 4| = 8.
A
The solutions are t = -2 and t = 6.
B
The solutions are t = 2 and t = -6.
C
The solutions are t = -1 and t = 5.
D
The solutions are t = 6 and t = 12.
Explanation
Solve 2t - 4 = 8 or 2t - 4 = -8 to get t = 6 or t = -2.
🚩 Report
Which statement must be true for the solution of |ax + b| = c to be the empty set?
A
If a is negative, the solution will be the empty set.
B
If b is negative, the solution will be the empty set.
C
If c is negative, the solution will be the empty set.
D
If c is positive, the solution will be the empty set.
Explanation
An absolute value cannot equal a negative number, so c must be negative.
🚩 Report
SKYDIVING: It takes approximately 6 minutes for a skydiver to land after she jumps out of a plane, give or take 30 seconds. What is the range of time, in seconds, it could take?
A
[330, 390]
B
[6, 30]
C
[300, 360]
D
[330, 360]
Explanation
Six minutes is 360 seconds. Thirty seconds less or more gives the interval [330, 390].
🚩 Report
Label both graphs with equations. Graph 1 has points at -2 and 4. Graph 2 has points at -9 and 3. Use A: |x - 1| = 3, B: |x - 3| = 5, C: |x - 1| = 6, D: |x + 3| = 6.
A
Graph 1: A; Graph 2: D
B
Graph 1: B; Graph 2: C
C
Graph 1: C; Graph 2: B
D
Graph 1: D; Graph 2: A
Explanation
The midpoint and distance are 1 and 3 for Graph 1, and -3 and 6 for Graph 2.
🚩 Report
Solve |n - 3| = 5 and choose the correct solution set.
A
n = -2 and n = 8
B
n = 2 and n = -8
C
n = -3 and n = 5
D
n = 3 and n = -5
Explanation
Set n - 3 equal to 5 and -5 to get n = 8 and n = -2.
🚩 Report
Solve |f + 10| = 1 and choose the correct solution set.
A
f = 9 and f = 11
B
f = -9 and f = -11
C
f = 1 and f = -1
D
f = 10 and f = -10
Explanation
Set f + 10 equal to 1 and -1 to get f = -9 and f = -11.
🚩 Report
Solve the equation |7 - 2q| = 3.
A
q = 2 and q = 5
B
q = -2 and q = -5
C
q = 1 and q = 3
D
No solution
Explanation
Solve 7 - 2q = 3 and 7 - 2q = -3 to get q = 2 and q = 5.
🚩 Report
Solve the equation |4x - 2| = 26.
A
x = 7 and x = -6
B
x = 6 and x = -7
C
x = 7 and x = 8
D
x = -6 and x = -8
Explanation
Solve 4x - 2 = 26 and 4x - 2 = -26 to get x = 7 and x = -6.
🚩 Report
Solve the equation |w + 1| = 5.
A
w = 4 and w = 6
B
w = -4 and w = 6
C
w = 4 and w = -6
D
w = -4 and w = -6
Explanation
Solve w + 1 = 5 and w + 1 = -5 to get w = 4 and w = -6.
🚩 Report
Solve the equation |n + 2| = -1.
A
n = 1 and n = -3
B
n = -1 and n = 3
C
Identity (Infinitely many solutions)
D
No solution (∅)
Explanation
An absolute value cannot be negative, so there is no solution.
🚩 Report
Solve the equation |m - 2| = 2.
A
m = 0 and m = 4
B
m = 2 and m = -2
C
m = 1 and m = 3
D
m = 0 and m = -4
Explanation
Solve m - 2 = 2 and m - 2 = -2 to get m = 4 and m = 0.
🚩 Report
Solve the equation |(-1/2)b - 2| = 10.
A
b = -16 and b = 24
B
b = 16 and b = -24
C
b = -8 and b = 12
D
b = 8 and b = -12
Explanation
Solve (-1/2)b - 2 = 10 and (-1/2)b - 2 = -10 to get b = -24 and b = 16.
🚩 Report
Solve the equation |-4d + 6| = 12.
A
d = -3/2 and d = 9/2
B
d = 3/2 and d = -9/2
C
d = -3 and d = 6
D
d = 3 and d = -6
Explanation
Solve -4d + 6 = 12 and -4d + 6 = -12 to get d = -3/2 and d = 9/2.
🚩 Report
Solve (n - 4)/8 = 3/2. If necessary, round to the nearest hundredth.
Explanation
Multiply by 8 to get n - 4 = 12, so n = 16.
🚩 Report
Solve x/12 = (2x - 5)/18. If necessary, round to the nearest hundredth.
A
-10
B
-3.75
C
0.83
D
10
Explanation
Cross multiply: 18x = 24x - 60, so x = 10.
🚩 Report
MIXTURE: Oscar makes fruit punch by mixing 8 parts cranberry juice to 3 parts pineapple juice. How many cups of pineapple juice are needed with 48 cups of cranberry juice?
A
11 cups
B
18 cups
C
24 cups
D
128 cups
Explanation
Use 8/3 = 48/p. Since 48 is 6 times 8, p = 6 × 3 = 18 cups.
🚩 Report
Ayita is making 12 gallons of a mixture that is 20% plant food and 80% water. Which proportions can be used to find the amount p of plant food? A: 20/80 = p/12. B: 20/100 = p/12. C: 80/100 = p/12. D: 20/p = 80/12. E: (12 - p)/12 = 80/100. Select all that apply.
A
B and E
B
A and B
C
B and D
D
C and E
Explanation
Plant food is 20% of the total, giving B. Water is 12 - p and 80% of the total, giving E.
🚩 Report
Solve the proportion 3/8 = 15/a. If necessary, round to the nearest hundredth.
A
a = 40
B
a = 2.8
C
a = 48
D
a = 3.6
Explanation
Cross multiply: 3a = 120, so a = 40.
🚩 Report
Solve the proportion t/2 = 6/12. If necessary, round to the nearest hundredth.
A
t = 36
B
t = 1
C
t = 4
D
t = 2.5
Explanation
Since 6/12 = 1/2, t/2 = 1/2 and t = 1.
🚩 Report
Solve the proportion 4/9 = 13/q. If necessary, round to the nearest hundredth.
A
q = 29.25
B
q = 5.78
C
q = 2.77
D
q = 36
Explanation
Cross multiply: 4q = 117, so q = 29.25.
🚩 Report
Solve (4v + 7)/15 = (6v + 2)/10. If necessary, round to the nearest hundredth.
A
v = 0.8
B
v = 2.5
C
v = -1.2
D
v = 3.6
Explanation
Cross multiply: 40v + 70 = 90v + 30, so 40 = 50v and v = 0.8.
🚩 Report
Solve (9b - 3)/9 = (5b + 5)/3. If necessary, round to the nearest hundredth.
A
b = -3
B
b = 4
C
b = -2
D
b = 1.5
Explanation
Cross multiply and simplify: 27b - 9 = 45b + 45, so b = -3.
🚩 Report
Solve (2n - 4)/5 = (3n + 3)/10. If necessary, round to the nearest hundredth.
A
n = 5
B
n = 11
C
n = -3
D
n = 8.5
Explanation
Cross multiply: 20n - 40 = 15n + 15, so n = 11.
🚩 Report
Solve 2/(g + 6) = 4/(5g + 10). If necessary, round to the nearest hundredth.
A
g = 0.67
B
g = 7
C
g = -4
D
g = 3.5
Explanation
Cross multiply: 10g + 20 = 4g + 24, so g = 2/3 ≈ 0.67.
🚩 Report
Solve the proportion 9/g = 15/10. If necessary, round to the nearest hundredth.
A
g = 6
B
g = 13.5
C
g = 5.67
D
g = 15
Explanation
Cross multiply: 90 = 15g, so g = 6.
🚩 Report
Solve the proportion 3/a = 1/6. If necessary, round to the nearest hundredth.
A
a = 2
B
a = 9
C
a = 18
D
a = 0.5
Explanation
Cross multiply: a = 18.
🚩 Report
Solve the proportion 6/z = 3/5. If necessary, round to the nearest hundredth.
A
z = 3.6
B
z = 10
C
z = 15
D
z = 2.5
Explanation
Cross multiply: 30 = 3z, so z = 10.
🚩 Report
Solve the equation 5a - 2b = 15 for a.
A
a = 3 + 2b/5
B
a = 15 + 2b/5
C
a = 3 - 2b/5
D
a = (15 - 2b)/5
Explanation
Add 2b and divide by 5: a = (15 + 2b)/5 = 3 + 2b/5.
🚩 Report
Solve 2v = (w + v)/t for v.
A
v = w/(2t - 1)
B
v = w/(2t)
C
v = 2tw - 1
D
v = 2t/w
Explanation
Multiply by t: 2tv = w + v. Then v(2t - 1) = w, so v = w/(2t - 1).
🚩 Report
The volume of a cylindrical jar is V = πr2 h. What formula should be used to find the height h?
A
h = πr2
B
h = √(V/(πr))
C
h = V/(πr2 )
D
h = V/r2
Explanation
Divide V = πr2 h by πr2 to get h = V/(πr2 ).
🚩 Report
A cylindrical jar has radius 1.5 inches and original volume 30 cubic inches. What height should a new jar have to increase the volume by 6 cubic inches?
A
h = 4.25 inches
B
h = 5.09 inches
C
h = 6.15 inches
D
h = 7.5 inches
Explanation
The new volume is 36. Using h = V/(πr2 ) gives 36/(π × 1.52 ) ≈ 5.09 inches.
🚩 Report
VIDEO GAMES: Ella models profit with P = 40c - 300, where c is the number of copies sold. Which equation gives c for a specific profit P?
A
c = (P + 40)/300
B
c = P/40 + 300
C
c = P/40 - 300
D
c = (P + 300)/40
Explanation
Add 300 and divide by 40: c = (P + 300)/40.
🚩 Report
COOKING: Adelina needs 96 cloves of garlic. Each bag contains 3 heads, and each head has about 8 cloves. What assumption must she make when calculating how many bags to buy?
A
Each head of garlic has exactly 8 cloves.
B
The chefs need 96 heads of garlic.
C
The chefs need 96 cloves of garlic.
D
Each bag has 3 heads of garlic.
Explanation
The number of cloves per head is approximate, so the calculation assumes exactly 8 cloves per head.
🚩 Report
How many bags of garlic should Adelina purchase if she needs 96 cloves, each bag has 3 heads, and each head has 8 cloves?
Explanation
Each bag contains 3 × 8 = 24 cloves, and 96 ÷ 24 = 4 bags.
🚩 Report
AGRICULTURE: A dairy cow produces 832 ounces of milk per day. About how many gallons does it produce per year? Use 1 cup = 8 ounces, 1 quart = 4 cups, and 1 gallon = 4 quarts.
A
6.5 gallons per year
B
2372.5 gallons per year
C
4357.2 gallons per year
D
303,680 gallons per year
Explanation
One gallon is 128 ounces. Thus 832/128 = 6.5 gallons per day, and 6.5 × 365 = 2372.5 gallons per year.
🚩 Report
Solve the equation x - 2y = 1 for y.
A
y = (x - 1)/2
B
y = (x + 1)/2
C
y = 2x - 1
D
y = (1 - x)/2
Explanation
Subtract x: -2y = 1 - x. Dividing by -2 gives y = (x - 1)/2.
🚩 Report
Solve the equation d + 3n = 1 for n.
A
n = (1 - d)/3
B
n = (d - 1)/3
C
n = 3 - d
D
n = (1 + d)/3
Explanation
Subtract d and divide by 3: n = (1 - d)/3.
🚩 Report
Solve the equation u = vw + z for v.
A
v = (u - z)/w
B
v = (u + z)/w
C
v = w/(u - z)
D
v = u - z - w
Explanation
Subtract z and divide by w: v = (u - z)/w. The source PDF incorrectly labels the left side of its answer choices as u.
🚩 Report
Solve the equation x = b - cd for c.
A
c = (x - b)/d
B
c = (b - x)/d
C
c = (x + b)/d
D
c = b - x - d
Explanation
Rearrange to cd = b - x, then divide by d: c = (b - x)/d.
