Given:
Total number of coins (Quarters and dimes) = 60
Total amount = $12.45
To find:
The number of quarters and dimes.
Solution:
Let x be the number of quarters and y be the number of dimes.
We know that,
1 quarter = 0.25 dollar
1 dime = 0.10 dollar
Total coins:
...(i)
Total amount:
...(ii)
From (i), we get
...(iii)
Putting this value in (ii), we get
![0.25x+0.10(60-x)=12.45](https://tex.z-dn.net/?f=0.25x%2B0.10%2860-x%29%3D12.45)
![0.25x+6-0.10x=12.45](https://tex.z-dn.net/?f=0.25x%2B6-0.10x%3D12.45)
![0.25x-0.10x=12.45-6](https://tex.z-dn.net/?f=0.25x-0.10x%3D12.45-6)
![0.15x=6.45](https://tex.z-dn.net/?f=0.15x%3D6.45)
Divide both sides by 0.15.
![x=\dfrac{6.45}{0.15}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B6.45%7D%7B0.15%7D)
![x=43](https://tex.z-dn.net/?f=x%3D43)
Putting x=43 in (iii), we get
![y=60-43](https://tex.z-dn.net/?f=y%3D60-43)
![y=17](https://tex.z-dn.net/?f=y%3D17)
So, the number of quarters is 43 and the number of dimes is 17.
Therefore, the correct option is b.