Use Cramer's rule to find the price per gallon of premium and regular gas

Question

You fill your car with 15 gallons of premium gasoline and fill up a 5 gallon gas can with regular gasoline for various appliances around the house. You pay the cashier $42. The price of regular gasoline(y) is 20 cents less per gallon than the price of premium gasoline(x). 

Answer 1

Likely the idea is to set up two equations with two unknowns, the apply Cramer's rule to solve the system (as opposed to using the elimination or substitution method.

 

I might start writing two equations converting everything to $, Using R and P (instead of x and y).

 

1 R = P - 1/5  (or $0.20)

2 5R + 15P = 42

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1a. 5P - 5R = 1 (eliminate the fraction and rewrite 1)

2a. 15P + 5R = 42

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Now apply Cramer's rule finding values for D, D_R, and D_P.

 

Just adding the equations looks a lot easier, but this is likely an exercise in applying Cramer's rule.