Question 1080739
(1) {{{ 10d + 5n + 25q = 100 }}}
(2) {{{ d + n + q = 10 }}}
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I have to look at 3 cases:
1 quarter
2 quarters
3 quarters
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Case 1:
{{{ q = 1 }}}
The equations are:
(1) {{{ 10d + 5n + 25*1 = 100 }}}
(2) {{{ d + n + 1 = 10 }}}
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(2) {{{ d = 9 - n }}}
(1) {{{ 10*( 9-n ) + 5n + 25 = 100 }}}
(1) {{{ 90 - 10n + 5n = 75 }}}
(1) {{{ 5n = 15 }}}
(1) {{{ n = 3 }}}
and
(2) {{{ d = 9 - n }}}
(2) {{{ d = 9 - 3 }}}
(2) {{{ d = 6 }}}
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There are:
1 quarter
3 nickels 
6 dimes
I don't have to go any further -this solves it
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check:
(1) {{{ 10d + 5n + 25q = 100 }}}
(1) {{{ 10*6 + 5*3 + 25*1 = 100 }}}
(1) {{{ 60 + 15 + 25 = 100 }}}
(1) {{{ 100 = 100 }}}
OK