Maria has dimes and nickels in ratio of 5:1. If she trades 2 dimes for 4 nickels the ratio goes to 9:4. How many dimes did she start with?

Question

Please show work! It’s a challenge question and I am over thinking the problem

Answer 1

Let d and n represent the original number of dimes and nickels. Then since the initial ratio was 5:1, d=5n.

After trading, she has d-2 dimes and n+4 nickels and 4(d-2)=9(n+4). By substituting, we get:

4(d-2)=9(n+4) -> 4(5n-2)=9(n+4) -> 20n-8=9n+36 -> 11n=44 -> n=4 and d=20

As a check, after trading she has 8 nickels and 18 dimes which is indeed a ratio of 9:4.