Question

Hanna has a change jar that contains 37.50 in quarters and half dollars She has 12 times as many half dollars as quarters. How many of each type of coin does she have?she has____quartersshe has_____ half dollars

Answer 1

`\begin{gathered} \text{Let x be the number of half dollar she has, and y the number of quarters she has.} \\ \text{therefore we get the following equations} \\ 0.5x+0.25y=37.5 \\ 12y=x \\ \text{If we replace the second equation in the first one, we get} \\ 0.5\cdot12y+0.25y=37.5 \\ 6y+0.25y=37.5 \\ 6.25y=37.5 \\ y=(37.5)/(6.25)=6\text{ so she got 6 quarters} \\ \text{if y=6 we have that} \\ x=12\cdot y=12\cdot6=72\text{ halfs dollars} \end{gathered}`