Word problems on the ACT often do not require particularly difficult algebra to solve. Most of the time, solving simple linear equations or using a formula such as D = R x T is all that is required. The key is to not be intimidated by the length of the description and to be able to pull out the important information and set up the correct equation/s.
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1. Write down what the question is asking. What do the answer choices represent? The number of donuts? The cost per person for an amusement park ride? This is usually in the last sentence of the word problem.
2. Assign variables to unknown quantities. Pick variables that are logical and clear. Let’s say a question is asking about the price of a child’s movie ticket versus an adult’s movie ticket. Choose “c” to represent the cost of one child’s ticket, and choose “a” to represent to cost of one adult’s ticket.
3. Go line-by-line. Pull out the key phrases and ‘translate’ them from English to Math. Look for these common words and phrases. Remember to pay special attention to subtraction and division since what comes first in the sentence does not necessarily come first in the expression (i.e. “4 less than x” = x – 4).
4. Set up equation/s. Your key phrases will tell you how the variables relate to each other. Be on the lookout for ways to set up more than one equation with the same two variables. If you have two equations with the same two variables, you can solve for either variable using Combination or Substitution.
5. Having trouble? Backsolve! If you are having a hard time setting up the equations, try to work backwards using the answer choices. If the answer choices represent the cost of the child’s movie ticket, start with choice (C) and ask yourself, what if C is correct? What else has to be true? The right answer will agree with the given numbers and the relationship between the variables that is described in the question stem. This is also an excellent way to check your work! If you think you’ve found the correct answer, plug it in to make sure.
Now check out this ACT math question for more practice on factors, multiples, and divisors.