SOLUTION: A purse contains 22 coins. Some of the coins are nickels and some are dimes. The total value of the coins is $1.45. How many dimes are in the purse? Write a system of equations, an

Question 979652: A purse contains 22 coins. Some of the coins are nickels and some are dimes. The total value of the coins is $1.45. How many dimes are in the purse? Write a system of equations, and then solve. State the system of equations, and then the solution.
Let:
n represent the number of nickels
d represent the number of dimes
Write two equations:
n+?=22 This equation is based on the number of coins.
0.05 +?d=1.45 This equation is based on the value of the money.
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!

The system of equation is

.

To solve it, express n from the first equation and substitute into the second one. You will get

n = 22 - d, --->

0.05*(22-d) + 0.1*d = 1.45,

Solve the last equation by simplifying it step by step:

1.10 - 0.05*d + 0.1*d = 1.45,

(0.1 - 0.05)*d = 1.45 - 1.10,

0.05*d = 0.35,

d = = 7.

Thus we find the number of dimes: d = 7.
Now, the number of nickels is d = 22 - 7 = 15.

Check: 5*15 + 7*10 = 75 + 70 = 145 = $1.45.

Answer. 15 nickels and 7 dimes.

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