SOLUTION: Hi Could you help me solve this problem If Austin has 13 nickels and dimes in his pocket, and they have a combined value of 105 cents, how many of each coin does he have?

Click here to see ALL problems on Word Problems With Coins

Question 1033646: Hi Could you help me solve this problem
If Austin has 13 nickels and dimes in his pocket, and they have a combined value of 105 cents, how many of each coin does he have?
Found 2 solutions by fractalier, ikleyn:
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
Call their numbers n and d. Then we can write
n + d = 13
The value equation for them is
5n + 10d = 105
Now multiply the top equation by 5 and subtract from the bottom equation...we get
5n + 10d = 105
-(5n + 5d = 65)
------------------
5d = 40
d = 8 dimes which means there are 13-8 =
n = 5 nickels

Answer by ikleyn(52848) (Show Source):
You can put this solution on YOUR website!
.
Hi Could you help me solve this problem
If Austin has 13 nickels and dimes in his pocket, and they have a combined value of 105 cents, how many of each coin does he have?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Solution 1

The condition leads to this system of equations n + c = 13, (1) (n = # of nickels, c = # of dimes). 5n + 10c = 105. (2) To solve it, express c = 13-n from (1) and then substitute it into (2). You will get 5n + 10*(13 - n) = 105. (3) It is just easy to solve it. From this point you can complete the solution on your own.

Solution 2

Let n be the number of nickels. Then the number of dimes is (13-n). The "value" equation is 5n + 10*(13 - n) = 105. (Notice that it is the same as the equation (3) above) Again, you can complete it yourself.