Equations With One Variable
Help Questions
SAT Math › Equations With One Variable
A rectangle has perimeter 50 cm. If the length $L$ is 3 more than twice the width $W$ ($L = 2W + 3$), what is $W$?
7
22/3
8
44/3
Explanation
Use $2L + 2W = 50$ with $L = 2W + 3$: $2(2W + 3) + 2W = 50 \Rightarrow 6W + 6 = 50 \Rightarrow 6W = 44$, so $W = 22/3$.
A phone plan charges a $5$ monthly fee plus $0.10$ per text. If the total cost $C$ in dollars is given by $C = 0.10t + 5$ and last month the bill was $12.50$, how many texts $t$ were sent?
65
70
75
80
Explanation
Solve $0.10t + 5 = 12.50$ to get $0.10t = 7.50$ and $t = 75$.
Seven more than four times a number equals 39. Which value of $x$ satisfies $4x + 7 = 39$?
6
7
8
9
Explanation
Subtract 7 to get $4x = 32$, then divide by 4 to find $x = 8$.
Solve for $x$: $\frac{3}{4}(x - 2) - \frac{1}{3}(x + 4) = 5$.
$\frac{94}{15}$
$\frac{47}{10}$
$\frac{94}{5}$
$\frac{47}{5}$
Explanation
Combine terms to get $\left(\frac{5}{12}\right)x - \frac{17}{6} = 5$, so $\left(\frac{5}{12}\right)x = \frac{47}{6}$ and $x = \frac{47}{6}\cdot\frac{12}{5} = \frac{94}{5}$. Distractors reflect miscombining constants or dividing by the reciprocal incorrectly.
To a 40-liter solution that is 25% acid, pure acid is added to obtain a solution that is 30% acid. How many liters of pure acid are added?
3
$\frac{7}{20}$
2
$\frac{20}{7}$
Explanation
Let $x$ be liters added; $\frac{10 + x}{40 + x} = 0.30$ leads to $10 + x = 12 + 0.30x$, so $0.70x = 2$ and $x = \frac{20}{7}$. Other options come from using the wrong percent or rounding.
Solve for $x$: $5(2x - 1) = 3(x + 7) + 4$.
$\frac{25}{7}$
5
$\frac{30}{7}$
$\frac{7}{30}$
Explanation
Distribute and combine to get $10x - 5 = 3x + 25$, so $7x = 30$ and $x = \frac{30}{7}$. Other choices come from inverting the fraction, omitting the $+4$, or guessing $x=5$.
A linear function passes through $(2, 7)$ and $(8, -5)$. What is the value of $y$ when $x = 0$?
-11
-1
1
11
Explanation
Slope $m = \frac{-5 - 7}{8 - 2} = -2$, so using $y = mx + b$ with $(2,7)$ gives $7 = -2(2) + b$, hence $b = 11$. Other choices come from sign errors in computing the slope or intercept.
Solve: $5(x - 2) = 3x + 4$.
-3
2
7
14
Explanation
Distribute and collect terms: $5x - 10 = 3x + 4 \Rightarrow 2x = 14 \Rightarrow x = 7$. The other choices reflect forgetting to divide by 2 (14), moving terms incorrectly (-3), or ignoring the constant 10 (2).
Solve for $x$: $\frac{x}{3} + 8 = 14$.
6
10
14
18
Explanation
Subtract 8 to get $\frac{x}{3} = 6$, then multiply by 3 to find $x = 18$. The other answers come from stopping at 6 or mixing the operations when isolating $x$.
An item has a 20% discount off the original price $p$, then a 12 dollar coupon is applied, and then 10% sales tax is added. If the final amount paid is 79.2 dollars, what is $p$?
90
105
114
120
Explanation
Write $1.10(0.80p - 12) = 79.2$. Then $0.80p - 12 = 72 \Rightarrow 0.80p = 84 \Rightarrow p = 105$; other options come from ignoring the coupon or tax or misordering operations.