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

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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) About Me  (Show Source):
You can put this solution on YOUR website!

The system of equation is

system%28n+%2B+d+=+22%2C%0D%0A0.05%2An+%2B+0.10%2Ad+=+1.45%29.

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 = 0.35%2F0.05 = 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.