Question 1006162
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
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(1) {{{ d = n + 15 }}}
(2) {{{ 5n + 10d = 420 }}} ( in cents )
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(1) {{{ -n + d = 15 }}}
Multiply both sides of (1) by {{{ 5 }}} and
add the equations
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(1) {{{ -5n + 5d = 75 }}}
(2) {{{ 5n + 10d = 420 }}}
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{{{ 15d = 495 }}}
{{{ d = 33 }}}
and
(1) {{{ d = n + 15 }}}
(1) {{{ 33 = n + 15 }}}
(1) {{{ n = 18 }}}
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{{{ 33 + 18 = 51 }}}
there were 51 coins in his pocket
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check:
(2) {{{ 5n + 10d = 420 }}}
(2) {{{ 5*18 + 10*33 = 420 }}}
(2) {{{ 90 + 330 = 420 }}}
(2) {{{ 420 = 420 }}}
OK