Winson's 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?  Choose the most appropriate option:
A) 0.8 B) 0.75 C) c) 8/9 D) 5/7 E) 6/8
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:Winson's shop runs a sale on goldfish and platys.   13x + 12y = 5.60 &lt;&lt;&lt;&lt;&lt; Equation 1   14x + 21y = 8.05 &lt;&lt;&lt;&lt;&lt; Equation 2   2x + 3y = 1.15 [Factor Out 7 from equation 2] &lt;&lt;&lt;&lt;&lt; Equation 3   8x + 12y = 4.6 [Multiply Equation 3 with 4]   5x = 1.0 [Equation 1 - Equation 2]   x = 0.2   3y = 1.15 - 0.4= 
<gadget id="calculator">1.15 - 0.4</gadget>
<output>0.75</output>
0.75 [Substitute for x in Equation 1]   y= 0.25   x/y = 0.2/0.25 = 20/25 = 4/5= 
<gadget id="calculator">4/5</gadget>
<output>4/5 = around 0.8</output>
0.8 [Answer A]   The whole thing must have taken me about 45 s :5/7
<result>D</result>
Winson's 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?