In a jar, the ratio of the number of dimes to the number of quarters is $3: 2$. If the total value of these coins is $\$ 4$, how many dimes are in the jar?

(Each dime is worth 10 cents, each quarter is worth 25 cents, and $\$ 1$ equals 100 cents.)
Since the ratio of the number of dimes to the number of quarters is $3: 2$, then we let the numbers of dimes and quarters be $3 k$ and $2 k$, respectively, for some positive integer $k$.

Since each dime is worth 10 cents, then the $3 k$ dimes are worth $10(3 k)=30 k$ cents.

Since each quarter is worth 25 cents, then the $2 k$ quarters are worth $25(2 k)=50 k$ cents.

Since the total value of the coins is $\$ 4$ which equals 400 cents, then $30 k+50 k=400$ or $80 k=400$, and so $k=5$.

Therefore, there are $3(5)=15$ dimes in the jar.

(Note that 15 dimes are worth 150 cents and $2(5)=10$ quarters are worth 250 cents, for a total of 400 cents, as required.)

ANSWER: 15