Question 184241
Let {{{c}}}= number of compacts bought
Let {{{i}}}= number of intermediates bought
Let {{{f}}}= number of full-sizes bought
given:
(1) {{{1500000 = 12000*c + 18000i + 24000f}}}
(2) {{{c = 2i}}}
(3) {{{c + i + f = 100}}}
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First divide both sides of (1) by {{{1000}}}
(1) {{{1500000 = 12000*c + 18000i + 24000f}}}
(1) {{{1500 = 12c + 18i + 24f}}}
Now divide both sides by {{{3}}}
(1) {{{500 = 4c + 6i + 8f}}}
Multiply both sides of (3) by {{{8}}}
(3) {{{8c + 8i + 8f = 800}}}
Subtract (1) from (3)
(3) {{{8c + 8i + 8f = 800}}}
(1) {{{-4c - 6i - 8f = -500}}}
(4) {{{4c + 2i = 300}}}
Substitute (2) in (4)
(4) {{{4*(2i) + 2i = 300}}}
(4) {{{8i + 2i = 300}}}
(4) {{{10i = 300}}}
(4) {{{i = 30}}}
and
(2) {{{c = 2i}}}
(2) {{{c = 60}}}
and
(3) {{{c + i + f = 100}}}
(3) {{{60 + 30 + f = 100}}}
(3) {{{f = 10}}}
They must purchase 60 compacts, 30 intermediates,
and 10 full size
check answer:
(1) {{{500 = 4c + 6i + 8f}}}
(1) {{{500 = 4*60 + 6*30 + 8*10}}}
(1) {{{500 = 240 + 180 + 80}}}
(1) {{{500 = 500}}}
OK