I have some quarters and some nickels. I have 20% as many quarters as nickels. I have $6.00 in total. I need to know the number of nickels. How do I solve this?
-CG
Let N be the number of nickels.....then the number of quarters are .20N
And we have the value of each nickel times their number plus the value of each quarter times their number equals the total value.......thus......
.05N + .25(.20N) = 6.00 simplify
.05N + .05N = 6.00
.1N = 6.00 divide by .1 on each side
N = 60 nickels
And the number of quarters = .20(60) = 12
if n = number of nickels and q = number of quarters, we have:
5n + 25q = 600
and
0.2q = n or q = n/0.2
Put this last back in to the first equation:
5n + n/0.2 = 600
5n + 5n = 600
10n = 600
n = 60
S0 there are 60 nickels and 12 quarters.
Check
$${\mathtt{60}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{25}} = {\mathtt{600}}$$
.
Let N be the number of nickels.....then the number of quarters are .20N
And we have the value of each nickel times their number plus the value of each quarter times their number equals the total value.......thus......
.05N + .25(.20N) = 6.00 simplify
.05N + .05N = 6.00
.1N = 6.00 divide by .1 on each side
N = 60 nickels
And the number of quarters = .20(60) = 12