you have only nickels and dimes. in total you have 65 coins and the value of these coins is $5.10. how many of each coin do you have?

Answer 1

Let

N = the number of nickels

D = the number of dimes

There are a total number of 65 coins.

Therefore

N + D = 65 (1)

Note that a nickel is worth $0.05 and a dime is worth $0.10.

The value of all the coins is $5.10. The nickels are worth $0.05*N and the dimes are worth $0.10*D.

Therefore

0.05N + 0.10D = 5.10

Multiply every term by 100.

5N + 10D = 510

Divide every term by 5.

N + 2D = 102 (2)

Subtract equation (1) from equation (2).

N + 2D - (N + D) = 102 - 65

D = 37 (There are 37 dimes)

From equation (1), obtain

N + 37 = 65

N = 65 - 37 = 28 (There are 28 nickels)

Answer:

There are 28 nickels and 37 dimes.

Check your answer.

N + D = 28 + 37 = 65 (correct)

28*$0.05 + 37*$0.10 = $1.40 + $3.70 = $5.10 (correct)