Question

When Jeremiah’s granddaughter was born, he started saving quarters and half dollars for her. After 2 years he had saved a total of $70.75 for her. If the number of quarters was 2 less than three times the number of half dollars, how many quarters and how many half dollars did he save?

Answer 1

57 half dollars and 169 quarters

Explanation:

We will need a system of equations to solve this problem.

Given that the number of quarters is 2 less than three times the number of half dollars, we have Q = 3H - 2

Thus, we have 0.25Q + 0.50H = 70.75 and Q = 3H - 2.

The second equation allows us to use substitution:

`0.25(3H-2)+0.50H=70.75\\0.75H-0.50+0.50H=70.75\\1.25H=71.25\\H=57`

We can plus this 57 into the second equation to find the number of quarters:

`Q = 3(57)-2\\Q=169`