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 Question from tom, a student: mrs. jhonson planned to spend $\$78$for fabric to make draperies. She found her fabric on sale at 20% less per yard than she expected and was able to buy her drapery fabric plus 4 extra yards for bedspread for$\$83.20.$ how much fabric had she planned to buy and what was the original cost per yard? ... i dont know this and how to turned them into equations by setting variables...could you help me?

Hi Tom.

Often it seems the hardest part of word problems is figuring out how to translate things into mathematical variables and equations. The math is sometimes quite easy after that. Don't be afraid of using lots of variables at first as you work things out.

Here's how I would parse the problem:

Mrs. Johnson planned to spend $78 for fabric to make draperies. So the total she planned to spend was$78. We need to keep reading...

She found her fabric on sale at 20% less per yard than she expected.

There is an expected rate and a sale rate. So let's use variables: E for expected cost per yard and S for sale cost per yard. The information above means that S = E - 20%, or in a more formal way: S = 0.80 $\times$ E

[She] was able to buy her drapery fabric plus 4 extra yards for breadspread for $83.20. Okay, so she bought the amount of fabric she needed for the draperies plus for extra yards. Let's say she intended to buy D yards for draperies. Then she actually bought D + 4 yards, right? The total cost she paid was$83.20. So this is the amount of yards she actually bought (D + 4 yards) times the sale rate (S dollars per yard). We can make an equation out of that:

What about that $78? Is that meaningful? Yes, because it equals the amount of material she intended to buy times the rate she intended by pay per yard. That is, ###$\$78 = D \times E$

You see Tom, we have three different equations using three variables. That is what we need to solve the problem - you have to have (at least) as many equations as variables in order to come up with the answer.

I leave it to you to complete the problem. If you are stuck solving this "system of equations" (also called "simultaneous equations"), then look up the "elimination method" or the "substitution method" in our Quick Search for help.

Cheers,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.