How to Translate Words into Equations on the ACT

By Mark Zegarelli

Some ACT Math questions give you information about what happens when you perform various operations on an unknown number. To answer these questions, you can let x (or any variable you choose) equal the number you’re looking for. Then build an equation and solve it using any of the methods you already know.


When you divide a certain number by 2 and then add 2, the number you end up with is the same as when you add 24 and then divide this result by 3. What is the number?

(A)    30

(B)    36

(C)    42

(D)    48

(E)    56

To begin, let x be the number you’re looking for. The first part tells you to divide x by 2 and then add 2:


The next part tells you to add 24 to x and then divide the result by 3:


The number you end up with is the same in both cases, so you can link these two expressions with an equal sign:


Now you have an equation that you can solve using any of the tools and tricks you know. Begin by multiplying every term here by the common denominator of 6 and simplify:


Now simplify and solve for x:


So the correct answer is Choice (B).