A Quick Brain Teaser

$11.60 is made up of only dimes and quarters. There are 32 more dimes than quarters. How many dimes and quarters are there?

Hint
Solve for the number of quarters, Q, and from that we can determine the number of dimes, D.
$$$D=Q+32$$$
Hint 2
$$$\$ 11.60=\$0.25Q+\$0.10D$$$
Solve for the number of quarters, Q, and from that we can determine the number of dimes, D. Based on the problem statement:
$$$D=Q+32$$$
$$$\$11.60=\$0.25Q+\$0.10D$$$
Combining the previous two equations:
$$$\$11.60=\$0.25Q+\$0.10(Q+32)$$$
$$$\$11.60=\$0.25Q+\$0.10Q+\$3.2$$$
$$$\$8.4=\$0.35Q$$$
Solving for the quarters:
$$$Q=\frac{\$8.4}{\$0.35}=24$$$
Now, solving for the dimes:
$$$D=Q+32=24+32=56$$$
24 Quarters & 56 Dimes