Question 704562
Let {{{ a }}} = pounds of 21% hamburger needed
Let {{{ b }}} = pound of 15% hamburger needed
given:
(1) {{{ a + b = 75 }}}
(2) {{{ ( .21a + .15b ) / 75 = .17 }}}
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(2) {{{ .21a + .15b = .17*75 }}}
(2) {{{ .21a + .15b = 12.75 }}}
(2) {{{ 21a + 15b = 1275 }}}
Multiply both sides of (1) by {{{ 15 }}} and
subtract (1) from (2)
(2) {{{ 21a + 15b = 1275 }}}
(1 ) {{{ -15a - 15b = -1125 }}}
{{{ 6a = 150 }}}
{{{ a = 25 }}}
and
(1) {{{ 25 + b = 75 }}}
(1) {{{ b = 50 }}}
25 pounds of 21% hamburger are needed
50 pound of 15% hamburger are needed
check:
(2) {{{ ( .21*25 + .15*50 ) / 75 = .17 }}}
(2) {{{ ( 5.25 + 7.5 ) / 75 = .17 }}}
(2) {{{ 12.75 / 75 = .17 }}}
(2) {{{ 12.75 = .17*75 }}}
(2) {{{ 12.75 = 12.75 }}}
OK