Mr. D has 10 more nickels than quarters. If he has a total of $3.80, how many quarters does he have?

Question

Mr. D has 10 more nickels than quarters. If he has a total of $3.80, how many quarters does he have?

Answer 1

Let N= #of nickels, Q = #of quarters

N = Q+10 (nickels is 10 more then quarters).

Each nickel is worth 5 cents. If you have 3 nickels you have 15 cents. If you have N nickels you have 5N cents.

Similarly for quarters, the number of cents for Q quarters is 25Q.

So,

5N + 25Q = 380 (note $3.80 has been converted to 380 cents).

Now substitute the value for N in terms of Q from the very 1st equation into the previous.

5 ( Q + 10) + 25 Q = 380

5Q + 50 +25Q = 380

30Q = 330

Q = 11

Since N = Q + 10, N = 11+10 = 21.

Number of quarters is 11 and number of nickels is 21.

11(25) = $2.75

21(5) = $1.05

Total = $3.80 (check)