ACT Practice Math Questions: Setting Up Algebraic Formulas

By Lisa Zimmer Hatch, Scott A. Hatch

Some questions on the ACT Math exam present you with a word problem that asks you to set up an algebraic formula that would solve the problem. Nervous? Don’t be. Instead, try flexing your formula-building muscles with the following practice questions.

Practice questions

  1. When asked how many years she had worked at her job, Leah responded, “Take the square root of 605, add it to the square of 5, and take 25 percent of the resulting sum.” Which of the following expresses Leah’s years on the job (L)?

    ACT_1301

  2. If doughnuts cost n dollars per dozen, which of the following expresses the cost of t doughnuts?

    ACT_1302

Answers and explanations

  1. The correct answer is Choice (E).

    Glance at the answers to make sure you know what this word problem is asking for before you start doing any math. It doesn’t want the solution to the equation but rather the equation itself. For these types of questions, working backward is often easier. “25 percent of the resulting sum” means 0.25 times the total of all else, so you can eliminate Choices (A) and (D). Neither multiplies by 0.25. Adding the square of 5 is simply + 25. Choice (C) is wrong because it multiplies rather than adds 25. And + 25 doesn’t belong under the square root sign, which means you can cross out Choice (B). Only Choice (E) remains.

  2. The correct answer is Choice (A).

    The easy way to do this problem is to plug in easy values for the variables. Let n = 1. Then find the cost of 12 doughnuts (so t = 12). If one dozen, or 12, doughnuts cost 1 dollar, the cost of t doughnuts is 1 dollar. Substitute 1 for n and 12 for t in the answers to see which one equals 1 dollar.

    When you substitute your values for the variables in Choice (A), you get 1 dollar:

    ACT_1303

    You can try the other answers to be sure, but Choice (A) is the only one that gives you 1 dollar when you make the substitutions.