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Is alligation method possible with the problem below? Thx!

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by Mormuse » Tue Apr 02, 2013 5:48 am
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
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by Brent@GMATPrepNow » Tue Apr 02, 2013 6:03 am
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
Currently: ratio of flour to baking soda is 10 to 1
Let F = pounds of flour
Let B = pounds of baking soda
So, F/B = 10/1
Cross multiply to get 10B = 1F
Rearrange to get 10B - F = 0

If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1
In this scenario, there are B+60 pounds of baking soda, and F pounds of flour.
So, F/(B+60) = 8/1
Cross multiply to get 8(B+60) = 1F
Expand: 8B + 480 = F
Rearrange to get 8B - F = -480

We now have
10B - F = 0
8B - F = -480

Subtract the red equation from the blue equation to get 2B = 480
So, B = 240

Since F/B = 10/1, and B = 240, we know that F = 2400

Finally, we'll use the fact that the ratio of sugar to flour is 5 to 8
In other words, S/F = 5/8
If F = 2400, we get S/2400 = 5/8
Solve for S to get S = 1500

Answer = C

Cheers,
Brent
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by GMATGuruNY » Tue Apr 02, 2013 8:06 am
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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hi

by Jeff@TargetTestPrep » Fri Jan 05, 2018 9:50 am
Mormuse 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
Since flour is the common item in both given ratios, we should make the number for flour the same in both ratios:

sugar to flour = 5 : 8 --> sugar to flour = 25 : 40

flour to baking soda = 10 : 1 --> flour to baking soda = 40 : 4

Thus:

sugar to flour to baking soda = 25x : 40x : 4x

If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1, and thus:

40x/(4x + 60) = 8/1

40x = 8(4x + 60)

5x = 4x + 60

x = 60

So, there are 25 x 60 = 1500 pounds of sugar stored in the room.

Answer: C

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