Question 1054839
Let {{{ n }}} = number of plain doughnuts
{{{ 15 - n }}} = number of glazed doughnuts
Let {{{ c }}} = cost of a glazed doughnut
{{{ c - 10 }}} = cost of a plain  doughnut
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(1) {{{ ( c - 10 )*n + c*( 15 - n ) = 465 }}} ( in cents )
(1) {{{ c*n - 10n + 15c - c*n = 465 }}}
(1) {{{ 15c - 10n = 465 }}}
(1) {{{ 15c = 10n + 465 }}}
(1) {{{ c = ( 2/3 )*n + 31 }}}
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I'll try {{{ n=3 }}}
(1) {{{ c = 2 + 31 }}}
(1) {{{ c = 33 }}}
and
{{{ c - 10 = 23 }}}
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(1) {{{ ( c - 10 )*n + c*( 15 - n ) = 465 }}} 
(1) {{{ 23*3 + 33*12 = 465 }}}
She bought 3 plain doughnuts
She bought 12 glazed doughnuts