Question 937628
Let {{{ a }}} = number of 5 rupee notes
Let {{{ b }}} = number of 10 rupee notes
Let {{{ c }}} = number of 20 rupee notes
Let {{{ d }}} = number of 50 rupee notes
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(1) {{{ b = 5a }}}
(2) {{{ b = 4c }}}
(3) {{{ b = 10d }}}
(4) {{{ 5a + 10b + 20c + 50d = 8400 }}}
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(1) {{{ a = b/5 }}}
(2) {{{ c = b/4 }}}
(3) {{{ d = b/10 }}}
By substitution:
(4) {{{ 5*(b/5) + 10b + 20*(b/4) + 50*(b/10) = 8400 }}}
Multiply both sides by {{{ 20 }}}
(4) {{{ 20b + 200b + 100b + 100b = 168000 }}}
(4) {{{ 420b = 168000 }}}
(4) {{{ b = 400 }}}
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(1) {{{ a = 400/5 }}}
(1) {{{ a = 80 }}}
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(2) {{{ c = 400/4 }}}
(2) {{{ c = 100 }}}
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(3) {{{ d = 400/10 }}}
(3) {{{ d = 40 }}}
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There are:
80 of the 5 rupee notes
400 of the 10 rupee notes
100 of the 20 rupee notes
40 of the 50 rupee notes
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check:
(4) {{{ 5a + 10b + 20c + 50d = 8400 }}}
(4) {{{ 5*80 + 10*400 + 20*100 + 50*40 = 8400 }}}
(4) {{{ 400 + 4000 + 2000 + 2000 = 8400 }}}
(4) {{{ 8400 = 8400 }}}
OK