SOLUTION: Another difficult question, please help. A factory produced some muffins. Half of the muffins were chocolate. The rest of the muffins were vanilla and blueberry in the ratio of 5

Question 1186897: Another difficult question, please help.
A factory produced some muffins. Half of the muffins were chocolate. The
rest of the muffins were vanilla and blueberry in the ratio of 5:7. There were
1 800 more chocolate muffins than blueberry muffins. What was the total number
of muffins produced by the factory?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
If 5 and 7 parts were half of the muffins, 5 and 7 being 12 parts, then the chocolate muffins (half of all the muffins) and another 12 parts of all the muffins.

RATIO chocolate : vanilla : blueberry 12 : 5 : 7

x, a common factor for each of the parts.
-----------1800 more chocolate than blueberry

24 total parts of 360 in each part

How Many Muffins

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

"The rest of the muffins were vanilla and blueberry in the ratio of 5:7"

Given that ratio...

Let 5x = # of vanilla muffins
Let 7x = # of blueberry muffins

(NOTE: That is almost always a good way to start on a problem where a ratio like 5:7 is given.)

"Half of the muffins were chocolate."

That means the number of chocolate muffins is equal to the total number of vanilla and blueberry muffins. So...

Let 12x = # of chocolate muffins

"There were 1800 more chocolate muffins than blueberry muffins."

Change to wording so it reads exactly like an algebraic equation:

The number of chocolate muffins was 1800 more than the number of blueberry muffins.

12x = 7x+1800

Solve for x using basic algebra. Then the answer (total number of muffins) is 24x.

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