Question 473003
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{ 10d + 25q = 785 }}} (in cents)
(2) {{{ d = 3q - 4 }}}
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Substitute (2) into (1)
(1) {{{ 10*(3q - 4) + 25q = 785 }}}
(1) {{{ 30q - 40 + 25q = 785 }}}
(1) {{{ 55q = 785 + 40 }}}
(1) {{{ 55q = 825 }}}
(1) {{{ q = 15 }}}
and, since
(2) {{{ d = 3q - 4 }}}
(2) {{{ d = 3*15 - 4 }}}
(2) {{{ d = 45 - 4 }}}
(2) {{{ d = 41 }}}
There are 41 dimes
check:
(1) {{{ 10d + 25q = 785 }}}
(1) {{{ 10*41 + 25*15 = 785 }}}
(1) {{{ 410 + 375 = 785 }}}
(1) {{{ 785 = 785 }}}
OK