Answer:
The number of dimes are 100 and number of quarters are 140.
Step-by-step explanation:
Let the number of dimes be 'd' and quarters be 'q'.
Given:
The sum of amount is $45.
The total number of coins are 240.
1 dime = $0.10
∴ 'd' dimes = [tex]\$0.10d[/tex]
1 quarter = $0.25
∴ 'q' quarters = [tex]\$0.25q[/tex]
Now, as per question:
[tex]d+m=240-----1\\0.1d+0.25q=45---2[/tex]
Multiplying equation (1) by -0.1 and adding the result to equation (2), we get:
[tex]-0.1d-0.1q=240\times -0.1\\-0.1d-0.1q=-24\\0.1d+0.25q=45\\-----------\\0.15q=21\\q=\frac{21}{0.15}=140\\\\d=240-q=240-140=100[/tex]
Therefore, the number of dimes are 100 and number of quarters are 140.
