SOLUTION: 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 t

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Question 1184949: 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?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
c of the chocolate puffs
w of the strawberry puffs



Gave away p number of puffs of each kind
c-p of the chocolate kept
w-p of the strawberry kept










Use E1 and E2 to equation expressions for p, and have

Using substitution from



.
.

This means c=1060-500







How many puffs remain?
Answer by ikleyn(52905)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~


            When I solve such problems,  I always try to find the simplest way to solve - - - and the best way to teach.

            Regarding this problem,  it can be easily solved using two simple equations instead of three;
            this way is simpler and,  THEREFORE,  is more preferable. 


Let  c  be the number of chocolate puffs, and

let  w  be the number of strawberry puffs.


The total was 1600 puffs, which gives you first equation

    c + w = 1600          (1)


After giving away, Bryan was left with 2/7 of the chocolate  puffs; hence, he gave away  chocolate puffs.

                   He    was left with 1/5 of the strawberry puffs; hence, he gave away  strawberry puffs.


He gave away equal number of both types of puffs; it gives you second equation

     = .     (2)


Multiply equation (2) by 35 (both sides).  You will get then

    25c = 28w.            (3)


Now you have the system of two equations (1) and (3).


From (1), express  c = 1060-w  and substitute it to equation (3).  You will get

    25*(1060-w) = 28w

    25*1060 - 25w = 28w

    25*1060 = 28w + 25w

       w    =  = 500.


So, originally, there were 500 strawberry puffs  and  1060-500 = 560 chocolate puffs.


Hence, the total number of puffs left was   +  = 2*80 + 100 = 260.    ANSWER

Solved and thoroughly explained.



Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


Let x be the number of chocolate puffs
Then 1060-x is the number of strawberry puffs

After giving away equal numbers of both, he was left with 2/7 of the chocolate puffs and 1/5 of the strawberry puffs. So 5/7 of the chocolate puffs is the same number as 4/5 of the strawberry puffs:



Multiply by the least common denominator (5*7=35) to clear fractions:






So he baked 560 chocolate puffs and 1060-560=500 strawberry puffs.

After giving some away, he was left with 2/7 of the chocolate puffs and 1/5 of the strawberry puffs.

(2/7)560=160
(1/5)500=100

ANSWER: The total number of puffs left was 160+100=260
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