Question 872392
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
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(1) {{{ n + d = 20 }}}
(2) {{{ 5n + 10d = 165 }}} ( in cents )
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(2) {{{ n + 2d = 33 }}}
Subtract (1) from (2)
(2) {{{ n + 2d = 33 }}}
(1) {{{ -n - d = -20 }}}
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{{{ d = 13 }}}
and, since
(1) {{{ n + d = 20 }}}
(1) {{{ n + 13 = 20 }}}
(1) {{{ n = 7 }}}
There are 7 nickels and 13 dimes
check:
(2) {{{ 5n + 10d = 165 }}}
(2) {{{ 5*7 + 10*13 = 165 }}}
(2) {{{ 35 + 130 = 165 }}}
(2) {{{ 165 = 165 }}}
OK