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Bryan baked a total of 1060 chocolate puffs and strawberry puffs. After giving away an equal number of both types of puffs, he was left with 2/7 of the chocolate puffs and 1/5 of the strawberry puffs. What was the total number of puffs left?

 Sep 21, 2021
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Let  c  be the number of chocolate puffs he baked and let  s  be the number of strawberry puffs he baked.

 

Since he baked a total of 1060 puffs, we can make the following equation

 

c + s  =  1060

 

Let  x  be the number of puffs he gave away for each type.

 

So since he was left with 2/7 of the chocolate puffs after giving away  x  chocolate puffs, we can say:

 

c - x  =  \(\frac27\)c

 

And since he was left with 1/5 of the strawberry puffs after giving away  x  strawberry puffs, we can say:

 

s - x  =  \(\frac15\)s

 

The total number of puffs left is going to be 1060 - 2x. So now we need to find  x  by solving this system of three equations.

 

s - x  =  \(\frac15\)s          ⇒          s - \(\frac15\)s  =  x          ⇒          \(\frac45\)s  =  x          ⇒          s  =  \(\frac54\)x

 

c - x  =  \(\frac27\)c          ⇒          c - \(\frac27\)c  =  x          ⇒          \(\frac57\)c  =  x          ⇒          c  =  \(\frac75\)x

 

 

c + s  =  1060              Now we can substitute  \(\frac54\)x  in for  s  and  \(\frac75\)x  in for  c

 

\(\frac75\)x  +  \(\frac54\)x  =  1060

 

\(\frac{53}{20}\)x   =   1060

 

x   =   1060 * \(\frac{20}{53}\)

 

x   =   400

 

And so the total number of puffs left  =  1060 - 2x  =  1060 - 2(400)  =  1060 - 800  =  260

 Sep 21, 2021

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