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ACT Math : How to find the solution to an equation

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Example Question #82 : Algebra

Translate into an algebraic expression:

Two fifths of the difference of five times a number and two equals six times the number.

Possible Answers:

$\frac{2}{5}(2x+5)=6x$

$\frac{2}{5}(2-5x)=6x$

$\frac{2}{5}(5x-2)=6x$

$\frac{2}{5}(2x-5)=6x$

$\frac{2}{5}(5x+2)=6x$

Correct answer:

$\frac{2}{5}(5x-2)=6x$

Explanation:

In order to translate the description into an algebraic expression, you must first form the difference (5x-2) , multiply it by $\frac{2}{5}$ , and then set the equation equal to , as follows:

$\frac{2}{5}(5x-2)=6x$

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Example Question #121 : How To Find The Solution To An Equation

A car averages miles per gallon. If gas costs $\$ 3.04$ per gallon, which of the following is closest to how much the gas would cost for this car to travel $1\textup{,}642$ typical miles?

Possible Answers:

$\$50$

$\$51$

$\$155$

$\$17$

$\$156$

Correct answer:

$\$156$

Explanation:

To solve this problem you should divide the total number of miles $\left ( 1\textup{,}642\right )$ by the miles per gallon $\left ( 32\right )$ , and then multiply by the cost of gas per gallon $\left ( \$3.04\right )$ . This gives you $\$155.99$ , which is closest to $\$156$ .

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Example Question #122 : How To Find The Solution To An Equation

When $\textup{w}= 6\textup{ and } \textup{z} = 4$ , by how much does the value of $3\textup{w}^{2}-2\textup{z}$ exceed the value of $2\textup{w}^{2} - 3\textup{z}$ ?

Possible Answers:

Correct answer:

Explanation:

You must plug in for $\textup{w}$ and for $\textup{z}$ , this means $3\textup{w}^{2}-2\textup{z}=$ $3\left ( 36\right )-2\left ( 4\right )=100$ and $2\textup{w}^{2}-3\textup{z}=2\left ( 36\right )-3\left ( 4\right )=60$

100-60=40

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Example Question #121 : Linear / Rational / Variable Equations

What is the value of $\textup{t}$ when $3\textup{t}+5=7\textup{t}-2$ ?

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{7}{10}$

$\frac{7}{4}$

$\frac{4}{7}$

Correct answer:

$\frac{7}{4}$

Explanation:

The first step is to subtract $\textup{3t}$ from both sides so you're left with $5=4\textup{t}-2$ . Next, you add to both sides, giving you $7=4\textup{t}$ . The final step is to divide by , giving you $\frac{7}{4}=\textup{t}$ .

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Example Question #124 : How To Find The Solution To An Equation

Karen has $\$7$ more than times as many dollars as Susan. Karen also has $\frac{1}{2}$ as many dollars as John would if he had more dollars. How many dollars does Susan have, relative to John?

Possible Answers:

$\frac{J}{4}$

3J -3

6J -4

J + 2

$\frac{J-12}{6}$

Correct answer:

$\frac{J-12}{6}$

Explanation:

First, set up our two equations. If Karen has seven dollars more than three times as many dollars as Susan, then K = 3S +7 . If Karen has half as many dollars as John would if he had two more dollars, then $K = \frac{J+2}{2}$ . The Substitution Property of Equality thus says that $3S +7 = \frac{J+2}{2}$ . Now, we simply solve for in terms of .

$3S +7 = \frac{J+2}{2}$

6S +14 = J+2

6S = J-12

$S = \frac{J-12}{6}$

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Example Question #125 : How To Find The Solution To An Equation

If the third day of the year is a Wednesday, what is the 165th day?

Possible Answers:

Wednesday

Thursday

Tuesday

Monday

Friday

Correct answer:

Thursday

Explanation:

If the third day is a Wednesday, then the first day is a Monday. 23 weeks will complete a cycle with the 161st day. Therefore, the fourth day past that, 165, is a Thursday.

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ACT Math : How to find the solution to an equation

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #82 : Algebra

Example Question #121 : How To Find The Solution To An Equation

Example Question #122 : How To Find The Solution To An Equation

Example Question #121 : Linear / Rational / Variable Equations

Example Question #124 : How To Find The Solution To An Equation

Example Question #125 : How To Find The Solution To An Equation

All ACT Math Resources

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