# Algebra: Equations

## Algebra: Equations

Read the following SAT test question and then select the correct answer.

Math problems require you to read carefully. Identify the bottom line, what the question is asking, and assess your options for solving the problem. There are often multiple ways to solve a problem, but you should be as efficient as possible. Choose a method to attack the problem, then loop back to make sure that you solved for the bottom line.

If  $\frac{24}{15} = \frac{4}{n}$, what is the value of 4n?

Bottom Line: 4n =

Assess your Options You could solve for n and multiply by 4, or you could find a way to solve the equation for 4n. The latter method will save you time because you do not have to do the extra step of multiplying by 4. Both ways will work, but on a timed test you should choose the faster method.

Attack the Problem: Go ahead and cross multiply so that you have the equation 24n = 15 × 4. In other words, 24n = 60. Now, if you were solving for n you would have to deal with a decimal or fraction. Instead, look at the equation that you have. You know that 24 and 60 are both multiples of 4, so it would be easier to solve for 4n than to solve for n. What do you have to multiply by 4 in order to get 24? 6. All you have to do is divide each side of your equation by 6, and you will get 4n = 10.

Loop Back: You solved for your bottom line, so you are ready to look at the answer choices.

(A) 6

(B) 10

(C) 12

(D) 30

(E) 60