Question 630935
{{{ .08*200 = 16 }}} pounds of potassium total
{{{ .3*200 = 60 }}} pounds of nitrogen total
{{{ .62*200 = 124 }}} pounds of phosphorus total
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Let {{{ a }}} = weight in pounds of 1st fertilizer
Let {{{ b }}} = weight in pounds of 2nd fertilizer
Let {{{ c }}} = weight in pounds of 3rd fertilizer
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{{{ .1a + .1b + 0*c = 16 }}}
{{{ .4a + .2b + .4c = 60 }}}
{{{ .5a + .7b + .6c = 124 }}}
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(1) {{{ a + b = 160 }}}
(2) {{{ 4a + 2b + 4c = 600 }}}
(3) {{{ 5a + 7b + 6c = 1240 }}}
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(1) {{{ a = 160 - b }}}
Substitute this into (2)
(2) {{{ 4*( 160 - b ) + 2b + 4c = 600 }}}
(2) {{{ 640 - 4b + 2b + 4c = 600 }}}
(2) {{{ -2b + 4c = 600 - 640 }}}
(2) {{{ 4c = 2b - 40 }}}
(2) {{{ c = b/2 - 10 }}}
Substitute (1) and (2) into (3)
(3) {{{ 5*( 160 - b ) + 7b + 6*( b/2 - 10 ) = 1240 }}}
(3) {{{ 800 - 5b + 7b + 3b - 60 = 1240 }}}
(3) {{{ 5b = 1240 - 800 + 60 }}}
(3) {{{ 5b = 500 }}}
(3) {{{ b = 100 }}}
and
(1) {{{ a = 160 - b }}}
(1) {{{ a = 160 - 100 }}}
(1) {{{ a = 60 }}}
and
(2) {{{ c = b/2 - 10 }}}
(2) {{{ c = 100/2 - 10 }}}
(2) {{{ c = 40 }}}
60 pounds of 1st fertilizer are needed
100 pounds of 2nd fertilizer are needed
40 pounds of 3rd fertilizer are needed
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You can check like this:
{{{ .1a + .1b + 0*c = 16 }}}
{{{ .1*60 + .1*100 = 16 }}}
{{{ 6 + 10 = 16 }}}
{{{ 16  = 16 }}}
OK- you can check (2) and (3)