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Cindy, Dorothy and Ellen each made an equal number of paper hearts for  a fund raising project. Cindy and Dorothy each sold some paper hearts Ellen sold 70 paper hearts. The 3 girls had a total of 85 paper hearts left. Cindy had \( {1 \over 4}{}{}\) as many paper hearts as Dorothy left while Ellen had 5 fewer paper hearts than Cindy left. How many paper hearts did Dorothy sell?

 Aug 24, 2021
edited by KourageKowardlyDog  Aug 24, 2021
 #1
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Cindy, Dorothy, and Ellen each made an equal number of paper hearts for a fund raising project. Cindy and Dorothy each sold some paper hearts Ellen sold 70 paper hearts. The 3 girls had a total of 85 paper hearts left. Cindy had 1/4  as many paper hearts as Dorothy left while Ellen had 5 fewer paper hearts than Cindy left. How many paper hearts did Dorothy sell?

 

Let each of them start with H hearts

Cindy sells C hearts so she is left with  H - c  hearts

Dorothy sells D hears so she is left with H - d  hearts

Ellen sells 70 so she is left with   H - 70 hearts 

 

Now make up equations for the other things you are told.

It will be easiest if you start with  "Ellen had 5 fewer paper hearts than Cindy left."

From that statement alone you can work out how many Cindy sells.

 

But you need the other facts too because you need to find what Dorothy sells.

 Aug 29, 2021
 #3
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Sorry if this was a late response.

 

Set they had equal number which is x, and

 Dorothy left y paper hearts.

  So,   \( {1 \over 4}{}{}\)y + y + \( {1 \over 4}{}{}\)y - 5 = 85   
                                  y = 60

  and  Ellen (left)  =  \({1 \over 4}{}{}\)y  - 5  =  \( {1 \over 4}{}{}\) * 60  -5  =10

   So  the number of them had are x = 10 + 70  = 80

   So   Dorothy (sell)   = 80 - 60  =20.

 

 

20  paper hearts.

 Sep 5, 2021
 #4
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Thanks!

KourageKowardlyDog  Sep 5, 2021

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