Question 241985
Let {{{d}}} = number of dimes he has
Let {{{q}}} = number of quarters he has
given:
(1){{{d + q = 10}}}
(2) {{{10d + 25q + 30 = 10q + 25d}}}
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Notice that on the right side, I make the quarters
worth {{{10}}} each and dimes worth {{{25}}} each
From (1):
(1) {{{q = 10 - d}}}
And, substituting:
(2) {{{10d + 25*(10 - d) + 30 = 10*(10 - d) + 25d}}}
{{{10d + 250 - 25d + 30 = 100 - 10d + 25d}}}
{{{-15d + 280 = 15d + 100}}}
{{{30d = 180}}}
{{{d = 6}}}
And, since
{{{q = 10 - d}}}
{{{q = 4}}}
He has 4 quarters
check answer:
(2) {{{10d + 25q + 30 = 10q + 25d}}}
{{{10*6 + 25*4 + 30 = 10*4 + 25*6}}}
{{{60 + 100 + 30 = 40 + 150}}}
{{{190 = 190}}}
OK