Solving word problems
Updated: Oct 25, 2019
Most students I work with say they really don't like/hate/don't understand/freeze up when they see word problems. Knowing how to decipher a word problem becomes easier with practice.
Here are some tips:
1. Underline the question. This will help you know what the variable(s) is/are to set up the equation.
2. Circle the relevant information, usually the numbers. Some word problems offer extraneous numbers...ask yourself, is this relevant to the question?
3. Set up the equation(s). Sometimes you will have a systems of equations. Usually, that is stated in the question.
Here are some practice examples:
1. Jenna has some pants and t-shirts in her closet totaling 24 together. She has twice as many t-shirts as pants. How many t-shirts does she have?
Jenna has some pants and t-shirts in her closet totaling 24 together. She has twice as many t-shirts as pants. How many t-shirts does she have?
Here I bolded 24 (you should circle) and underlined the question.
Variables are need to label WHAT YOU DON'T KNOW, so
p is the number or pants t is the number of t-shirts
p + t = 24
We were also told she has twice as many t-shirts as pants, so to make an equation,
we have to multiple the number of pants by 2 to equal the number of t-shirts.
2p = t
Notice the t in each equation. I can use substitution, with the goal of having only 1 variable to solve. So, if I substitute 2p (because 2p = t) for t in the first equation, I get
p + 2p = 24
3p = 24 divide both sides by 3
p = 8
there are 8 pairs of pants. But we need to know how many t-shirts. There are twice as many t-shirts as pants, so 2p = t
2 (8) = t
16 = t there are 16 t-shirts. Which answers the question!
Try another one:
2. Mara has 117 dollars. She wants to give 2/3 of this money to her siblings and save the rest for a jacket she saw at the mall. If she wants to share the 2/3 evenly with each of her 3 siblings, how much will each one get?
Circle 117, 2/3 and 3
Underline how much will each one get
Try to solve it before you look ahead at the answer.
Step 1, find out what 2/3 of 117 is.
Step 2, find out what 1/3 of that is.
Step 1: 2/3 of 117 means 2/3 x 117 so 2/3 x 117 = 78
(if you aren't allowed to use a calculator, use fraction multiplication: 2/3 x 117/1 = 234/3 = 78)
Step 2: 1/3 of 78 because you're sharing (dividing) 78 by the 3 siblings. 78/3 =26
You're done! Each sibling gets $26.