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A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?

A. 7
B. 14
C. 21
D. 28
E. 35
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Re: Algebra [#permalink]  17 May 2012, 05:45
kashishh wrote:
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. i f he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?
A. 7
B. 14
C. 21
D. 28
E. 35

7C+6P=95
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for C & P to solve so that eqn is satisfied

The least value of C for which equation gets satisfied is 5
i.e. 7*5+6*10=35+60=95
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kashishh wrote:
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 95 cookies, what is the minimum number of chocolate chip cookies he makes?

A. 7
B. 14
C. 21
D. 28
E. 35

Say x is the number of chocolate cookies and y is the number of peanut cookies Bob makes. Notice that since chocolate cookies are in batches of 7 and peanut cookies are in batches of 6 then x must be a multiple of 7 and y must be a multiple of 6.

Given: x+y=95 --> y=95-x. We want to minimize x, so we need to find the minimum value of a multiple of 7 (x) that must be subtracted from 95 to get a multiple of 6 (y). The minimum value turns out to be 35=5*7: 95-35=60=6*10.

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