Question 533419
They mean that she has 3 times as many quarters as dimes
plus 1 more quarter.
For example, if she had 5 dimes, then she would have
{{{ 3*5 }}} = 15 quarters plus 1 more quarter = 16 quarters
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As for your problem,
Let {{{q}}} = number of quarters she has
Let {{{d}}} = number of dimes she has
given:
(1) {{{ q = 3d + 1 }}}
(2) {{{ 25q + 10d = 280 }}} ( in cents )
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Divide both sides of (2) by {{{5}}}
(2) {{{ 5q + 2d = 56 }}}
Substitute (1) into (2)
(2) {{{ 5*( 3d + 1 ) + 2d = 56 }}}
(2) {{{ 15d + 5 + 2d = 56 }}}
(2) {{{ 17d = 51 }}}
(2) {{{ d = 3 }}}
and, since
(1) {{{ q = 3d + 1 }}}
(1) {{{ q = 3*3 + 1 }}}
(1) {{{ q = 10 }}}
She has 10 quarters and 3 dimes