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In the storage room of a certain bakery, the ratio of sugar

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In the storage room of a certain bakery, the ratio of sugar [#permalink]

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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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Re: In the storage room of a certain bakery, the ratio of sugar [#permalink]

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\(\frac{S}{F}=\frac{5}{8}\)

\(\frac{F}{B}=\frac{10}{1}\)

\(\frac{F}{(B+60)}=\frac{8}{1}\)

Therefore...

\(F=8*(B+60)=10*B\)

=> \(8*B+480=10B\)

=> \(B=240lbs\)

=> \(F=10*B=10*240=2400lbs\)

=> \(S=\frac{5}{8}*F=\frac{5}{8}*2400=1500lbs\)

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Re: In the storage room of a certain bakery, the ratio of sugar [#permalink]

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nave81 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


Sugar:Flour = 5:8 = 25:40;
Flour:Soda = 10:1 = 40:4;

Thus we have that Sugar:Flour:Soda = 25x:40x:4x.

Also given that 40x/(4x+60) = 8/1 --> x=60 --> Sugar = 25x = 1,500.

Answer: C.
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Re: In the storage room of a certain bakery, the ratio of sugar [#permalink]

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New post 10 Oct 2017, 12:57
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?

Many problems on the GMAT lend themselves to algebraic solutions, but sometimes those solutions can elude students in the heat of the moment on the test. Let's use this example to illustrate a useful technique to use when the algebra eludes us and we're confronted with a word problem that asks for a specific value, in this case pounds of sugar, and provides answer choices that are in numeric order - Backsolving. First label your answer choices as referring to the sought after value as such:

Pounds Sugar
A. 600
B. 1200
C. 1500
D. 1600
E. 1750

Then, we can simply work through the constraints of the problem. To maximize efficiency try to estimate if you need a high or low value first and/or eliminate any logically impossible choices. If you are unable to do so, a good tactic is beginning with answer choice C, because based on the outcome of that test at a minimum you should be able to determine whether the proper value should be higher or lower.

C. 1500 > Set up a proportion of 1500/x = 5/8 to find that based on the given ratios there would be 2400 pounds of flour and subsequently 240 pounds of baking soda. Now, add 60 pounds to that 240 pounds to get 300 hypothetical pounds of baking soda. 2400/300 equals the 8/1 ratio dictated by the problem, so C is the correct choice and without needing any complex algebra.

For those of you who can do the algebra referenced in the other replies to this post, do it! Algebra is often the fastest way to solve a problem like this one. However, if you are having issues with the algebra on any long-winded word problems asking for a specific value such and the answer choices are numeric values in ascending or descending order, consider backsolving as an alternative approach!
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Re: In the storage room of a certain bakery, the ratio of sugar [#permalink]

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New post 15 Oct 2017, 20:00
Bunuel wrote:
nave81 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


Sugar:Flour = 5:8 = 25:40;
Flour:Soda = 10:1 = 40:4;

Thus we have that Sugar:Flour:Soda = 25x:40x:4x.

Also given that 40x/(4x+60) = 8/1 --> x=60 --> Sugar = 25x = 1,500.

Answer: C.


Hi Bunuel

Why can't we do 10x/x+60=8/1

Please help!!

Thanks

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Re: In the storage room of a certain bakery, the ratio of sugar [#permalink]

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New post 15 Oct 2017, 21:28
zanaik89 wrote:
Bunuel wrote:
nave81 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


Sugar:Flour = 5:8 = 25:40;
Flour:Soda = 10:1 = 40:4;

Thus we have that Sugar:Flour:Soda = 25x:40x:4x.

Also given that 40x/(4x+60) = 8/1 --> x=60 --> Sugar = 25x = 1,500.

Answer: C.


Hi Bunuel

Why can't we do 10x/x+60=8/1

Please help!!

Thanks


Because x (a multiplier) you get from that won't be the same one you could then use for Sugar:Flour ratio. So, first you should get the ratio Sugar:Flour:Soda = 25:40:4 and then assign a common multiplier x to that.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the storage room of a certain bakery, the ratio of sugar [#permalink]

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New post 17 Oct 2017, 11:55
nave 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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Re: In the storage room of a certain bakery, the ratio of sugar   [#permalink] 17 Oct 2017, 11:55
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