## 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?

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__**Hint**

**Hint**

Solve for the number of quarters, Q, and from that we can determine the number of dimes, D.

$$$D=Q+32$$$

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__**Hint 2**

**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