SOLUTION: Hi At a bakery the ratio of cakes to muffins was 3 to 1. The bakery sold half of total of cakes and muffins. Out of the total 5/6 were cakes. In the end there were 24 muffins lef

Question 1195277: Hi
At a bakery the ratio of cakes to muffins was 3 to 1. The bakery sold half of total of cakes and muffins. Out of the total 5/6 were cakes. In the end there were 24 muffins left.
How many cakes were sold.
Thanks

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39628) (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

At a bakery the ratio of cakes to muffins was 3 to 1.
So x = muffins and 3x = cakes

The bakery sold half of total of cakes and muffins.
total (originally) was x+3x = 4x; half were sold
Number sold: (1/2)(4x) = 2x

Out of the total 5/6 were cakes. (The wording here is poor; we must assume the statement means that 5/6 of the total items SOLD were cakes.)
Number of cakes sold: (5/6)(2x) = (5/3)x

In the end there were 24 muffins left.
5/6 of the items sold were cakes, so 1/6 of them were muffins.
Number of muffins sold: (1/6)(2x) = (1/3)x.
The original number of muffins was x; the number sold was (1/3)x; so the number unsold was (2/3)x.
Since the number of muffins unsold was (2/3)x = 24, the original number of muffins was 24(3/2) = 36.

How many cakes were sold.
The original number of muffins was x=36, so the original number of cakes was 3x=108.
The number of cakes sold was (5/3)x = 60.

ANSWER: 60

CHECK:
Originally.... 108 cakes, 36 muffins, 144 total
Number of items sold: half of 144 = 72
Number of cakes sold: (5/6) of 72 = 60
Number of muffins sold: (1/6) of 72 = 12
Number of muffins unsold: 36-12 = 24

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