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A cake recipe uses a constant ratio of 2 teaspoons vanilla

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A cake recipe uses a constant ratio of 2 teaspoons vanilla [#permalink] New post 05 Apr 2010, 10:52
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A cake recipe uses a constant ratio of 2 teaspoons vanilla extract to 1 ounce chocolate. If the original recipe, which serves four people, is altered proportionally to yield a cake that serves six people, how many ounces of chocolate will be used in the larger cake?

(1) The original recipe calls for exactly five teaspoons of vanilla extract.

(2) If the original recipe were altered proportionally to yield a cake that serves eight people, ten teaspoons of vanilla extract would be used.

please explain algebraically
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Re: ratios [#permalink] New post 05 Apr 2010, 11:25
apoorvasrivastva wrote:
A cake recipe uses a constant ratio of 2 teaspoons vanilla extract to 1 ounce chocolate. If the original recipe, which serves four people, is altered proportionally to yield a cake that serves six people, how many ounces of chocolate will be used in the larger cake?

(1) The original recipe calls for exactly five teaspoons of vanilla extract.

(2) If the original recipe were altered proportionally to yield a cake that serves eight people, ten teaspoons of vanilla extract would be used.

please explain algebraically

for every 2 teaspoons of vanilla, 1 ounce of choclate is used

st 1) five teaspoons of vanilla exteact will serve 4 people, 7.5 tea spoons will server 6 people. so 7.5/2 ounces of choclater is needed. Sufficient
st 2) 10 teaspoons of vanilla exteact will serve 8 people, 7.5 tea spoons will server 6 people. so 7.5/2 ounces of choclater is needed. Sufficient
D
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Re: ratios [#permalink] New post 05 Apr 2010, 16:45
Vo = Vanilla original
Co = Chocolate original
V6 = Vanilla in cake for 6 people
C6 = Chocolate in cake that serves six people

We're trying to find the value of the variable C6.

Vo/Co = 2/1

This makes a cake that serves four people. To make a cake that serves six people, we must take the original amounts and multiply them by 1.5. However, we don't know the original amounts yet.

S1. Vo = 5
therefore Co = 2.5

We take Co and multiply by 1.5 to get C6:

C6 = 2.5 * 1.5 = 3.75
S

S2. 2*Vo = 10
Vo = 5
Co = 2.5

Again we take Co and multiply by 1.5 to get C6:

C6 = 3.75
S

Answer: D
Re: ratios   [#permalink] 05 Apr 2010, 16:45
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