Question 978555
Let {{{ d }}} = the number of dimes she spends
Let {{{ n }}} = the number of nickels she spends
(1) {{{ d + n = 8 }}}
(2) {{{ n = d + 4 }}}
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(2) {{{ -d + n = 4 }}}
Add (1) and (2)
{{{ 2n = 12 }}}
{{{ n = 6 }}}
and
(1) {{{ d + n = 8 }}}
(1) {{{ d + 6 = 8 }}}
(1) {{{ d = 2 }}}
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She has left:
{{{ 18 - n }}} nickels
{{{ 22 - d }}} dimes
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The value of what she has left is:
{{{ 5*18 - 5n = 5*( 18 - 6 ) }}}
{{{ 5*12 = 60 }}} cents in nickels
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{{{ 10*22 - 10d = 10*( 22 - 2 ) }}}
{{{ 10*20 = 200 }}} cents in dimes
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She has $2.60 left
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check the answer:
She spent 
{{{ 5n + 10d = 5*6 + 10*2 }}}
{{{ 30 + 20 = 50 }}} cents spent
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{{{ 260 + 50 = 310 }}}
She started with $3.10
{{{ 5*18 + 10*22 = 90 + 220 }}}
{{{ 90 + 220 = 310 }}}
She started with $3.10 
OK