Word Problem - Linear Systems

Question

Ken asked a friend to rent him a video game and as a joke the friend rented one that he didn’t think Ken would like. He was right. So Ken paid his friend the rental cost of $6.15 (including taxes) but he paid him using only nickels ($0.05) and dimes ($0.10). If there were 3 more dimes than nickels, how many of each coin did Ken give his friend?

Answer 1

This can be solved with a system of equations, but there is another way. First subtract the three extra dimes ($0.30) from $6.15 to get $5.85 for an equal number of dimes and nickels. Now consider that 1 dime plus 1 nickel is $0.15. Dividing $5.85 into groups of $0.15 gives an answer of 39. So there are 39 nickels and 39 + 3 or 42 dimes.