Given:
Total amount Rachelle has = $4.75
She has four more nickels than dimes and twice as many quarters as dimes.
To find:
The number of each kind of coin.
Solution:
Let the number of dimes be x. So,
Number of nickels = x+4
Number of quarters = 2x
We know that, 1 nickel = $0.05, 1 dime = $0.10 and 1 quarter = $0.25.
Total amount Rachelle has = $4.75.
[tex]0.05(x+4)+0.10x+0.25(2x)=4.75[/tex]
[tex]0.05x+0.20+0.10x+0.50x=4.75[/tex]
[tex]0.65x+0.20=4.75[/tex]
Subtract both sides by 0.20.
[tex]0.65x=4.75-0.20[/tex]
[tex]0.65x=4.55[/tex]
Divide both sides by 0.65.
[tex]x=\dfrac{4.55}{0.65}[/tex]
[tex]x=7[/tex]
Now,
Number of dimes = 7
Number of nickels = 7+4 = 11
Number of quarters = 2(7) = 14
Therefore, the number of dimes, nickels and quarters are 7, 11 and 14 respectively.
