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# help

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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

#1
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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