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Test PrepACTMathWord Problems

ACT Math Skill Review: Word Problems


Some of the problems on the ACT Math test will be presented as word problems. Sometimes the wording is so dense that it’s easy to forget you are in the math test at all! Indeed, for many of these problems, the most difficult thing about doing them is translating them into math. The actual computation is often pretty straightforward. These questions are testing your ability to set up an equation based on the information in the word problem, thus applying math skills to everyday situations.

Key points to remember:

  • Read the entire problem! Don’t try to solve anything until you get a feel for the whole question.
  • Orient yourself by making note of the information that is given throughout the problem.
  • Label variables with what they stand for.
  • Determine exactly what the problem is asking (and then underline it).
  • Work out the answer.
  • Double-check to make sure your answer makes sense. Check your answer against the original word problem, not your equation!

It takes practice to translate verbal descriptions of a mathematical relationship into actual math terms. Here’s a look at some examples:

Verbal Description Math Translation
Nine less than the total of a number and 2 e6.PNG
The ratio of 9 more than x to 3 e2.PNG
Sarah has four more dollars than Kevin e3.PNG
The average of the weights of three children is 80 pounds e4.PNG
James has twice the number of apples as Kristen but one-third the number of apples as Larry. e7.PNG

Examples

  1. The product of two consecutive negative even integers is 24. What is the smaller of the two numbers?

  2. Gloria’s washing machine is broken. Since her machine is pretty old, she doesn’t want to spend more than $100 for repairs. A service call will cost $35 and the labor will be an additional $20 per hour. There are no other charges. What is the maximum number of hours that the repair person can work without the total cost exceeding $100?

Answers and Explanations

  1. The correct answer is A. First, evaluate the question. Since the two numbers are negative and nonconsecutive, you know that they will be two apart (for example, -2 and -4) and, as a result, one number will be two greater than the other. (Hint: with this information in hand, you can also eliminate choice E which isn’t even negative. You could also eliminate choice B given that it’s not even, another requirement of your answer.) So, we can call the first number n and the second number n + 2. The question states that the product of the two numbers is 24. Thus, (n)(n + 2) = 24. Now we solve for n:

    ans11.PNG

    Thus, n = -6 or 4. Since the question stated that the numbers were negative, the answer can’t be n = 4. If n = -6, n + 2 = -4 and the two numbers are -6 and -4. The question asks for the smaller of the two numbers, which is -6. 
     
  2. The correct answer is J. Let h equal the maximum number of hours the repair can take. Write out an equation based on the information given ($35 plus $20 per hour for h hours equals $100):

    ans21.PNG

    Thus, the answer must be J. Note, if you forgot about the $35 for a service call, you might be tempted by choice K. However, it’s important to remember this fee must be paid no matter how long the call takes.


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