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A baker made a combination of chocolate chip cookies and pea
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14 Jun 2018, 14:23
14 Jun 2018, 14:23
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Question Stats:
74% (01:59) correct
25% (02:54) wrong based on 63 sessions
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A baker made a combination of chocolate chip cookies and peanut butter cookies for a school bake sale. His recipes only allow him to make chocolate chip cookies in batches of 7, and peanut butter cookies in batches of 6. If he made exactly 95 cookies for the bake sale, what is the minimum possible number of chocolate chip cookies that he made?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
Re: A baker made a combination of chocolate chip cookies and pea
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03 Jul 2018, 00:32
03 Jul 2018, 00:32
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sandy wrote:
A baker made a combination of chocolate chip cookies and peanut butter cookies for a school bake sale. His recipes only allow him to make chocolate chip cookies in batches of 7, and peanut butter cookies in batches of 6. If he made exactly 95 cookies for the bake sale, what is the minimum possible number of chocolate chip cookies that he made?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
Here let x = no. of chocolate cookie
and y = peanut butter cookie
We have from the statement
7x + 6y = 95
Let us consider the value of x=1; but it doesnot satisfy the equation
The above equation satisfy only when x = 5, which is the minimum value
i.e. 7 * 5 + 6 *10 =95
Now the chocolate cookie he make in the batch of 7, so the minimum no. of chocolate cookie he made = 7 * 5 =35
Re: A baker made a combination of chocolate chip cookies and pea
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05 Jul 2018, 03:07
05 Jul 2018, 03:07
Expert Reply
Explanation
The equation for the situation described is 7x + 6y = 95, where x stands for the number of batches of chocolate chip cookies and y stands for the number of batches of peanut butter cookies.
It looks as though this equation is not solvable, because there are two variables and only one equation. However, since the baker can only make whole batches, x and y must be integers, which really limits the possibilities.
Furthermore, the question asks for the minimum number of chocolate chip cookies the baker could have made. So, try 1 for x and see if you get an integer for y (use your calculator when needed!):
\(7(1) + 6y = 95\)
\(6y = 88\)
\(y = 14.6\)…
Since this did not result in an integer number of batches of peanut butter cookies, this situation doesn’t work. Try 2, 3, 4, etc. for x. (Don’t try values out of order—remember, there might be more than one x value that works, but you need to be sure that you have the smallest one!)
The smallest value that works for x is 5:
\(7(5) + 6y = 95\)
\(6y = 60\)
\(y = 10\)
Remember that you need the minimum number of chocolate chip cookies, not batches of cookies.
Since the minimum number of batches is 5 and there are 7 cookies per batch, the minimum number of chocolate chip cookies is 35.
Hence option E is correct!
The equation for the situation described is 7x + 6y = 95, where x stands for the number of batches of chocolate chip cookies and y stands for the number of batches of peanut butter cookies.
It looks as though this equation is not solvable, because there are two variables and only one equation. However, since the baker can only make whole batches, x and y must be integers, which really limits the possibilities.
Furthermore, the question asks for the minimum number of chocolate chip cookies the baker could have made. So, try 1 for x and see if you get an integer for y (use your calculator when needed!):
\(7(1) + 6y = 95\)
\(6y = 88\)
\(y = 14.6\)…
Since this did not result in an integer number of batches of peanut butter cookies, this situation doesn’t work. Try 2, 3, 4, etc. for x. (Don’t try values out of order—remember, there might be more than one x value that works, but you need to be sure that you have the smallest one!)
The smallest value that works for x is 5:
\(7(5) + 6y = 95\)
\(6y = 60\)
\(y = 10\)
Remember that you need the minimum number of chocolate chip cookies, not batches of cookies.
Since the minimum number of batches is 5 and there are 7 cookies per batch, the minimum number of chocolate chip cookies is 35.
Hence option E is correct!
