Question 1012106
How many meters of cloth ?
Price / meter ?
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Let {{{ p }}} = unit price in Rs/meter
Let {{{ c }}} = meters of cloth actually purchased
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(1) {{{ p*c = 1600 }}}
(2) {{{ ( p - 40 )*( c + 2 ) = 1600 }}}
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(1) {{{ p = 1600/c }}}
and
(2) {{{ p*c - 40c + 2p - 80 = 1600 }}}
(2) {{{ p*c + 2p - 40c = 1680 }}}
(2) {{{ p*( c + 2 ) - 40c = 1680 }}}
(2) {{{ ( 1600/c )*( c + 2 ) - 40c = 1680 }}}
(2) {{{ 1600 + 3200/c - 40c = 1680 }}}
(2) {{{ 3200/c - 40c = 80 }}}
(2) {{{ 80/c - c = 2 }}}
(2) {{{ 80 - c^2 = 2c }}}
(2) {{{ c^2 + 2c - 80 = 0 }}}
(2) {{{ ( c + 10 )*( c - 8 ) = 0 }}} ( by inspection )
{{{ c = 8 }}} ( must be positive )
and
(1) {{{ p = 1600/c }}}
(1) {{{ p = 1600/8 }}}
(1) {{{ p = 200 }}}
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She purchased 8 meters of cloth
The price/meter was Rs 200
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check:
(2) {{{ ( p - 40 )*( c + 2 ) = 1600 }}}
(2) {{{ (200 - 40 )*( 8 + 2 ) = 1600 }}}
(2) {{{ 160*10 = 1600 }}}
(2) {{{ 1600 = 1600 }}}
OK