Answer:
Number of nickels = 6
number of dimes = 9
number of quarters =12
Step-by-step explanation:
Let 'q' be the number of quarters and 'n' be the number of nickels
and 'd' be the number of dimes
twice as many quarters as nickels
[tex]q=2n[/tex]
three more dimes than nickels.
[tex]d=3+n[/tex]
1 nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
4.20 dollars = 420 cents
[tex]5n+10d+25q=420[/tex]
replace q and d in the above equation
[tex]5n+10(3+n)+25(2n)=420[/tex]
[tex]5n+30+10n+50n=420[/tex]
[tex]65n+30=420[/tex]
Subtract 30 from both sides
[tex]65n=390[/tex]
divide both sides by 65
n=6
Number of nickels = 6
number of dimes = [tex]3+n=3+6=9[/tex]
number of quarters = [tex]2n=2(6)= 12[/tex]
