Problem Solving

Hi All,

We're told that a pet shop runs a sale on goldfish and platys, one customer buys 13 goldfish and 12 platys for $5.60, while another buys 14 goldfish and 21 platys for $8.05. We're asked for the ratio of the price of a goldfish to the price of a platys. This question can be solved in a couple of different ways, including System Algebra.

We're given information to form 2 equations:
13G + 12P = $5.60
14G + 21P = $8.05

If we 'divide' the second equation by 7, we get...
2G + 3P = $1.15

We can then 'multiply' by -4....
-8G - 12P = -$4.60

And combine that result with the first equation...
13G + 12P = $5.60
-8G - 12P = -$4.60
-----------------------
5G = $1.00
G = $0.20

We can then plug in the value of G to find the value of P:
2(0.20) + 3P = $1.15
0.40 + 3P = 1.15
3P = .75
P = .25

Thus, the ratio of G to P is .2 to .25 = 20:25 = 4/5 = .8

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

AAPL wrote: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

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