Question 962378
Let {{{ a }}} = number of $1 bills
Let {{{ b }}} = number of $5 bills
Let {{{ c }}} = number of $10 bills
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(1) {{{ b = a + 4 }}}
(2) {{{ a + 5b + 10c = 246 }}}
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There are 3 unknowns, but only 2
possible equations, so I have to 
do a little extra work
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Substitute (1) into (2)
(2) {{{ a + 5*( a + 4 ) + 10c = 246 }}} 
(2) {{{ a + 5a + 20 + 10c = 226 }}}
(2) {{{ 6a + 10c = 226 }}}
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{{{ c = 22 }}} and {{{ a = 1 }}} does not work, so
I'll try {{{ c = 19 }}} and {{{ a = 6 }}}
That gives me:
(2) {{{ 6*6 + 10*19 = 226 }}}
(2) {{{ 36 + 190 = 226 }}}
(2) {{{ 226 = 226 }}}
(1) {{{ b = a + 4 }}}
(1) {{{ b = 6 + 4 }}}
(1) {{{ b = 10 }}}
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there are:
6 of the $1 bills
10 of the $5 bills
19 of the $10 bills
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check:
(2) {{{ a + 5b + 10c = 246 }}}
(2) {{{ 6 + 5*10 + 10*19 = 246 }}}
(2) {{{ 6 + 50 + 190 = 246 }}}
(2) {{{ 246 = 246 }}}
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hope I got it