Let us bear in mind the equivalent value of these coins:
One dime = $0.10
One quarter = $0.25
Let x = number of dimes
y = number of quarters
Since the boy has 70 coins in total, we can say that:
x + y = 70 (can be written as x = 70 – y)
Since the boy has a total of $12.40, we can say that:
0.10x + 0.25y = 12.40
To solve this problem, we need to solve this system of equation. We have to substitute the value of x as written in the first equation (x = 70 –y)
0.10(70 – y) + 0.25y = 12.40
7 – 0.10y + 0.25y = 12.40
0.15y = 5.40
y = 36
X = 70 – 36
X = 34
Therefore, the boys has 34 dimes and 36 quarters. To check our answer, we just have to check if his money would total $12.40.
34 dimes = $3.40
36 dimes = $9.00
Total $12.40