claudayst wrote:In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 8, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
A. 600
B. 1200
C. 1500
D. 1600
E. 1750
Let S=sugar, F=flour, and B=baking soda.
Ratios can be MULTIPLIED:
S/B = S/F * F/B.
In the equation above, the value of F cancels out, leaving only S/B.
Since S/F = 5/8 and F/B = 10/1, we get:
S/B = 5/8 * 10/1 = 25/4.
Since F/B = 10/1, F = 10B.
Thus, F/B = (10B)/B.
When amount of baking soda increases by 60 pounds, the new ratio = (10B)/(B+60).
Since the new ratio is 8 to 1, we get:
(10B)/(B+60) = 8/1
10B = 8B + 480
2B = 480
B = 240.
Since B=240 and S/B = 25/4, we get:
S/240 = 25/4
S = 1500.
The correct answer is
C.
Alligation is a good approach when we know (one ingredient)/(total ingredients).
Since such a fraction is not given here, I wouldn't recommend alligation for this problem.
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