```Question 87411
n = number of nickels
d = number of dimes
q = number of quarters
{{{n + d + q = 130}}}
{{{n = 3.5q}}}
{{{q = .5d}}}
{{{3.5d + d + .5d = 130}}}
{{{5d = 130}}}
{{{d = 26}}}
{{{n = 3.5*26}}}
{{{n = 91}}}
{{{q = .5*26}}}
{{{q = 13}}}
To find how much money he has, find {{{5n}}}, {{{10d}}}, and {{{25q}}}
{{{91*5 + 26*10 + 13*25}}}
{{{455 + 260 + 325}}}
The answer is 1040 cents, or \$10.40
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In this case,
n = number of nickels
d = number of dimes
q = number of quarters
as before, but what is known is how much money he has
and not the total number of coins
{{{10d + 5n + 25q = 1765}}} (in cents)
{{{q = n - 11}}}
{{{d = 6q}}}
Solve the 1st equation for n
{{{n = q + 11}}}
Now find d and n in {{{10d + 5n + 25q = 1765}}} in terms of q
{{{10*6q + 5(q + 11) + 25q = 1765}}}
{{{60q + 5q + 25q + 55 = 1765}}}
{{{90q = 1710}}}
{{{q = 19}}}
{{{d = 6q}}}
{{{d = 114}}}
{{{n = q + 11}}}
{{{n = 19 + 11}}}
{{{n = 30}}}
The answer is 19 quarters, 114 dimes, and 30 nickels
You can check answer by plugging values for d, n, and q into
the original equation```