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?
+9465 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
