SOLUTION: Hi A B and C had 181 cookies at first. A gave away 20% of her cookies while B bought 28 more cookies. C also bought more cookies and had 4 times as many as before. Then the ratio

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi A B and C had 181 cookies at first. A gave away 20% of her cookies while B bought 28 more cookies. C also bought more cookies and had 4 times as many as before. Then the ratio       Log On

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Question 1147027: Hi
A B and C had 181 cookies at first. A gave away 20% of her cookies while B bought 28 more cookies. C also bought more cookies and had 4 times as many as before. Then the ratio of the number of cookies A B C had was 2:5:8 respectively. How many cookies did B have at first.
thanks
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the numbers for each person be A, B, and C. Then the given information tells us

(1) A+B+C = 181

(2) (4/5)A : B+28 : 4C = 2:5:8

Use the ratios in (2) to get B and C in terms of A and substitute in (1).

(Of course you could also get A and C in terms of B, or A and B in terms of C....)

B in terms of A:

%284%2F5%29A%2F%28B%2B28%29+=+2%2F5

2B%2B56+=+4A

B%2B28+=+2A

B+=+2A-28

C in terms of A:

%284%2F5%29A%2F%284C%29+=+2%2F8+=+1%2F4

%284%2F5%29A%2FC+=+1

C+=+%284%2F5%29A

Substitute and solve for A:

A+%2B+%282A-28%29+%2B+%284%2F5%29A+=+181

%2819%2F5%29A+-+28+=+181

%2819%2F5%29A+=+209

A+=+%285%2A209%29%2F19+=+5%2A11+=+55

Use this value of A to find B and C:

B+=+2A-28+=+110-28+=+82

C+=+%284%2F5%29A+=+44

Original numbers of cookies:
A = 55
B = 82
C = 44

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "a", "b" and "c" be the numbers of cookies that A, B and C had originally.


The first equation is


    a + b + c = 181.    (1)


After all events, A had  0.8a cookies,  B had (b+28)  and C had 4c cookies.


We are given this long proportion  0.8a : (b+28) : 4c = 2 : 5 : 8.


It means that

    0.8a = 2x,

    b+28 = 5x

    4c = 8x

for some unknown number x.


From these equations,  


    a = %282x%29%2F0.8,             (2)

    b = 5x - 28           (3)

    c = 2x.               (4)


Substitute it into equation (1). You will get


    %282x%29%2F0.8 + (5x-28) + 2x = 181.


Now solve this equation and find "x".


Then find "a", "b" and "c" from (2), (3) and (4).


Check if your answer are INTEGER numbers.

Just instructed / and completed.