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: [tex]x+y=60[/tex] ...(i)
Total amount: [tex]0.25x+0.10y=12.45[/tex] ...(ii)
From (i), we get
[tex]y=60-x[/tex] ...(iii)
Putting this value in (ii), we get
[tex]0.25x+0.10(60-x)=12.45[/tex]
[tex]0.25x+6-0.10x=12.45[/tex]
[tex]0.25x-0.10x=12.45-6[/tex]
[tex]0.15x=6.45[/tex]
Divide both sides by 0.15.
[tex]x=\dfrac{6.45}{0.15}[/tex]
[tex]x=43[/tex]
Putting x=43 in (iii), we get
[tex]y=60-43[/tex]
[tex]y=17[/tex]
So, the number of quarters is 43 and the number of dimes is 17.
Therefore, the correct option is b.
