Janet has 10 coins consisting of nickels, dimes, and quarters. Seven of the coins are either dimes or quarters, and eight of the coins are either dimes or nickels. How many dimes does Janet have?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Solution 1

Since Janet has 10 coins, seven of which are dimes and quarters, then three coins are nickels.

Since eight coins are nickels or dimes, then five are dimes.

Thus Janet has 5 dimes.

ANSWER: (D)

## Solution 2

If Janet has $n$ nickels, $d$ dimes and $q$ quarters, we can write

$$
\begin{aligned}
n+d+q & =10 \\
d+q & =7 \\
n+d & =8
\end{aligned}
$$

Subtracting equation (2) from equation (1), we get $n=3$. Substituting this in (3), we get $d=5$.

Thus, Janet has 5 dimes.

ANSWER:

(D)

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