A pet shop runs a sale on goldfish and platys. If one customer buys 1

Question

A pet shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?

A) 0.8
B) 0.75
C) 8/9
D) 5/7
E) 6/8

A) 0.8
B) 0.75
C) 8/9
D) 5/7
E) 6/8

AmrithS · Accepted Answer

The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?

In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!

Here's the working:

13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2

2x + 3y = 1.15   <<<<< Equation 3

8x + 12y = 4.6

5x = 1.0

x = 0.2

3y = 1.15 - 0.4 = 0.75

y = 0.25

x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8

The whole thing must have taken me about 45 s :D

mcmoorthy · Answer

Hi bhandariavi,

I tried this method and it worked....

I went by the answer choices.

took answer choice A) 0.8

Assumed x to be 8p and y to be 10p and substituted in 13x + 12y=5.6 and got the anwer as 224p=5.6 since 224 is a multiple of 56 there exists a common number p which should make the ratio to be true ( which is 1/40 in this case) and hence  Option A.

Kudos if you like this Post

bhandariavi · Answer

thanks AmrithS. Thanks to mcmoorthy as well.

ScottTargetTestPrep · Answer

We can let g = the price of 1 goldfish and p = the price of 1 platy and create the following equations:

13g + 12p = 5.6

and

14g + 21p = 8.05

Subtracting the first equation from the second, we have:

g + 9p = 2.45

g = 2.45 - 9p

Substituting for g back in the first equation, we have:

13(2.45 - 9p) + 12p = 5.6

31.85 - 117p + 12p = 5.6

31.85 - 5.6 = 117p - 12p

26.25 = 105p

0.25 = p

Since g = 2.45 - 9p, then g = 2.45 -9(0.25) = 0.2. Thus, the ratio of the price of goldfish to platys is

0.2/0.25 = 20/25 = 4/5 =0.8

Answer: A

KarishmaB · Answer

13G + 12P = 5.6
14G + 21P = 8.05

The equations are somewhat harder to work with so let's simplify them. Second equation can be simplified by dividing by 7 to get
2G + 3P = 1.15

Now multiply it by 4 to get 
8G + 12P = 4.6

and subtract from the first equation to get 
5G = 1 which means G = 0.2
Substitute G in any equation above to get P = 0.25

\frac{G}{P} = \frac{0.2}{0.25} = \frac{4}{5} = 0.8

Answer (A)

A pet shop runs a sale on goldfish and platys. If one customer buys 1

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A pet shop runs a sale on goldfish and platys. If one customer buys 1

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