



 
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:
So the total she planned to spend was $78. We need to keep reading...
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
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: $\$83.20 = (D + 4) \times S$ Now we get to the question:
Ah, so these are two things we already have variables for: the amount of fabric she originally planned to buy (D yards) and the original cost per yard she expected to pay (E dollars per yard). So the question is asking us for D and E. Let's now assemble the equations we know. $S = 0.80 \times E$
 


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