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 [Factor Out 7 from equation 2] <<<<< 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 = 0.75 [Substitute for x in Equation 1]

y = 0.25

x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]

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

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