Tackling Word Problems on the ACT
Even the strongest Math student can be troubled by the occasional tough word problem. It’s important not to rush when you read these types of questions. Make sure to read methodically and be confident you understand each part of the problem before you move on. Many students find themselves setting up equations and solving algebraically before they’ve even understood what the question is really asking!
Make sure to circle the question at the end of the word problem. You typically want to define whatever the question is asking for as x. It is also good practice to write down what you defined x to be. Sometimes, it might be easier to let something else be x. In those situations, always write down what the final answer you are looking for is, to remind yourself not to stop at solving for x. For example, if x is the length of a side of a square and the question asks for the perimeter, the final answer would be given by 4x.
One of the ways you can quickly sharpen your word problem skills is to practice translating English into Math. Certain words and phrases commonly occur in word problems and knowing the Math processes they represent will help you gain confidence.
Addition: increased by, more than, combined, together, total of, sum, added to
Subtraction: decreased by, minus, less, difference between/of, less than, fewer than
Multiplication: of, times, multiplied by, product of, increased/decreased by a factor of
Division: per, out of, ratio of, quotient of, percent (divide by 100)
Equals: is, are, was, were, will be, gives, yields, sold for
Make sure that you name variables after what they stand for so you can easily remember them. For example, if a problem says “Julie’s age is four years less than Sarah’s,” it is easier to write it as “J = S – 4” than as “x = y – 4”. You can always choose variables for unknown quantities.
Remember that with Subtraction and Division the order matters so read carefully so you know what is being subtracted or divided from what! For example, a common mistake to make with the above example would be to translate it as “J = 4 – S”. The order the words appear in English in a sentence is not necessarily the order in which they should appear in Math.
If translation and setting up algebraic equations is not your strong suit, you may also want to consider using one of two Math strategies: Picking Numbers or Backsolving.
Picking Numbers is a great strategy when there are variables in the question stem (like, a, x, n, etc.) and in the answer choices. Instead of setting up an equation, you simply pick nice, easy low numbers for the variables (such as 2, 3, 4, etc.) and plug them in, finding a solution. Once you have a solution, you plug the SAME numbers into the answer choices. Whatever matches your answer choice must be correct!
Backsolving is a great strategy when there are numbers in the answer choices. Instead of picking numbers for variables, you simply work backwards by plugging in each answer choice as if it’s correct. It’s a little bit like checking your work as you go! When backsolving, make sure to start with answer choice (C), typically the middle value, because the answer choices are usually listed in ascending order. That way, if you find the number is too small, you can then try (D) or (E). If (C) is too big, then try (A) or (B).
When practicing these pesky word problems, look for opportunities to Pick Numbers and Backsolve. It may seem awkward at first, but having multiple ways of solving can help on Test Day when you get stuck.