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When To Simplify Algebraic Expressions

Word problems on the SAT can be particularly challenging because, when it comes to math, our minds have been trained to think in numbers. When a problem introduces variables it is easy to become confused. One solution is to take out the variables in a word problem and replace them with numbers that are easy to work with.

Sample Problem

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?

  1. 299m + 261j ≥ 1,000
  2. 299m + 261j >1,000
  3. 299/m + 261/j ≥ 1,000
  4. 299/m + 261/j > 1,000

This math sample problem comes directly from the CollegeBoard website. The first step to solving this problem is to look for clues in the language. “Meet or exceed” indicates the solution should include ≥ 1,000. So that immediately eliminates options B and D. If it is easier to see the problem with numbers, plug in the number 3 for cups of milk and 4 for cups of juice. To determine how much you should drink you would multiply 3 by 299 and add it to 4 multiplied by 261. You don’t even need to solve the problem to see that you don’t use any division, so the correct answer must be  A.  

Plugging in Numbers

When you need to plug in numbers to make a problem clearer, avoid using 0,1, and even 2. While these numbers are easy to work with they have special rules that may result in the wrong answer. Instead choose numbers that work well with the numbers given in the problem. If the problem introduces the number 6 choose 3 or 12 to work with. The faster you can work with numbers in your head, the faster you will arrive at the answer.

Keep in mind you may have to plug the numbers into the solutions to find the correct answer. Often, the SAT gives an equation as a solution. If you choose to work with numbers instead of variables, you will have to fill in the numbers to find the coordinating solution.

Using the Clues

It can take time to simplify algebraic equations with numbers, so look for other clues in the word problem that will help you identify the solution. Words that indicate more or less or equal to can be very helpful. When you just can’t make the variable make sense, start plugging in numbers. While it has the potential to take more time, it is better than not finding an answer.

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