Question

There are 23 coins in a bank. All the coins are dimes and quarters. The total value of the coins is $3.80. How many dimes are there? How many quarters?
Write the system of equations that would be used to solve this problem.

Answer 1

The answer is 13 dimes and 10 quarters.

Let d be the number of dimes and q the number of quarters.

Since there are 23 coins (all dimes and quarters) in a bank, then the equation is:
d + q = 23
Since the value of 1 quarter is $0.25 and the value of 1 dime is $0.10, if the total value is $3.80, then the equation will be:
0.10d + 0.25q = 3.80 

Now, we have the system of equations:
d + q = 23
0.10d + 0.25q = 3.80 
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Rearrange the first equation:
d = 23 - q
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Substitute d from the first equation into the second equation:
0.10 * (23 - q) + 0.25q = 3.80

0.10 * 23 - 0.10 * q + 0.25 q = 3.80
2.30 + 0.15q = 3.80
0.15q = 3.80 - 2.30
0.15q = 1.50
q = 1.50 / 0.15
q = 10
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Now when we know the number of quarters, it is easy to calculate the number of dimes using the first equation:
d = 23 - q
d = 23 - 10
d = 13

Answer 2

Let q = quarter

Let d = dime

Here is your system:

q + d = 23

0.25q + 0.10d = 3.80

Take it from here.