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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?
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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.