SOLUTION: Hi
jack sold cookies, cakes and muffins in chocolate or butter flavor. He sold 140 more cookies than cakes at the fair. 1/5 of the cookies and 2/ 3 of the cakes sold were chocolat
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Question 1105262: Hi
jack sold cookies, cakes and muffins in chocolate or butter flavor. He sold 140 more cookies than cakes at the fair. 1/5 of the cookies and 2/ 3 of the cakes sold were chocolate. He sold an equal number of chocolate cake s and cookies. He also sold an equal number of butter cakes and muffins. The number of cakes sold was 3/4 the number of muffins sold.
How many more butter flavored than chocolate flavor ed cookies cakes and muffins were sold.
Can this be solved with 2 variables.
thanks
Found 2 solutions by stanbon, greenestamps:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jack sold cookies, cakes and muffins in chocolate or butter flavor.
He sold 140 more cookies than cakes at the fair.
O = A + 140
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1/5 of the cookies and 2/ 3 of the cakes sold were chocolate.
Chocolate = (1/5)O+(2/3)A
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He sold an equal number of chocolate cakes and cookies.
O = chocA
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He also sold an equal number of butter cakes and muffins.
bA = M
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The number of cakes sold was 3/4 the number of muffins sold.
A = (3/4)M
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How many more butter flavored than chocolate flavored cookies cakes and muffins were sold.
Can this be solved with 2 variables.
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It looks like it can't be solved with any number of variables.
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Cheers,
Stan H.
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Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
It can be solved with only one variable....
Represent the numbers of chocolate cookies, chocolate muffins, chocolate cakes, butter cookies, butter muffins, and butter cakes, respectively, with the matrix
The fact that he sold 140 more cookies than cakes is the last piece of information we will use.
Let's see what the other information tells us to reduce the number of variables.
(1) 1/5 of the cookies sold were chocolate. That means the number of butter cookies sold is 4 times the number of chocolate cookies:
(2) 2/3 of the cakes sold were chocolate. That means the number of chocolate cakes is 2 times the number of butter cakes:
(3) The number of chocolate cookies and chocolate cakes is the same:
(4) The number of butter cakes and butter muffins is the same:
(5) The number of cakes is 3/4 the number of muffins:
Everything is now in terms of a single variable. We can use the fact that the number of cookies was 140 more than the number of cakes to find the number of each item he sold.
He sold...
40 chocolate cookies;
60 chocolate muffins;
40 chocolate cakes;
160 butter cookies;
20 butter muffins; and
20 butter cakes
The answer to the specific question that was asked is (I think) the difference between the total number of butter items and the total number of chocolate items; that difference is
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