Question 1158536
Nickels are 5c each
dimes are 10c each
quarters are 25c each
loonies?
Let {{{ x }}} = the value in cents of 1 loony
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d = 4n }}}
(2) {{{ q = 3n }}}
(3) number of loonies = {{{ n - 3 }}}
(4) {{{  n + d + q + n - 3 = 69 }}}
(5) {{{ 5n + 10d + 25q + x*( n - 3 ) = 1460 }}} ( in cents )
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I have 4 unknowns and 4 equations, so it's solvable
Add (1) and (2)
{{{ d + q = 7n }}}
Plug this result into (4)
(4) {{{  n + d + q + n - 3 = 69 }}}
(4) {{{  n + 7n + n - 3 = 69 }}}
(4) {{{ 9n = 72 }}}
(4) {{{ n = 8 }}}
and
(1) {{{ d = 4n }}}
(1) {{{ d = 4*8 }}}
(1) {{{ d = 32 }}}
and
(2) {{{ q = 3n }}}
(2) {{{ q = 3*8 }}}
(2) {{{ q = 24 }}}
and
Number of loonies = 
{{{ n - 3 = 8 - 3 }}}
{{{ n - 3 = 5 }}}
He has:
8 nickels
32 dimes
24 quarters
5 loonies
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(5) {{{ 5n + 10d + 25q + x*( n - 3 ) = 1460 }}} ( in cents )
(5) {{{ 5*8 + 10*32 + 25*24 + x*( 8 - 3 ) = 1460 }}} ( in cents )
(5) {{{ 40 + 320 + 600 + 5x = 1460 }}} ( in cents )
(5) {{{ 5x = 500 }}}
(6) {{{ x = 100 }}}
A loony is worth 100c or $1