Question 168617
{{{f}}}= amount Fred gets
{{{g}}}= amount Grace gets
{{{a}}}= amount Aaron gets
Given:
(1) {{{g = 2f}}}
(2) {{{a = 3g}}}
(3) {{{a + f + g = 6750}}}
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From (1) 
(4){{{f = g/2}}}
Now substitute (2) and (4) into (3)
(3) {{{a + f + g = 6750}}}
(4) {{{3g + g/2 + g = 6750}}}
Multiply both sides by {{{2}}}
(5) {{{6g + g + 2g = 13500}}}
(6) {{{9g = 13500}}}
(7) {{{g = 1500}}}
Substitute this back in (2)
(2) {{{a = 3g}}}
(8) {{{a = 3*1500}}}
(9) {{{a = 4500}}}
Substitute (7) into (4)
(4) {{{f = g/2}}}
{10) {{{f = 1500/2}}}
(11) {{{f = 750}}}
Fred gets $750, Grace gets $1500, Aaron gets $4500
check:
(1) {{{g = 2f}}}
(2) {{{a = 3g}}}
(3) {{{a + f + g = 6750}}}
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(1) {{{g = 2f}}}
(12) {{{1500 = 2*750}}}
(13) {{{1500 = 1500}}}
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(2) {{{a = 3g}}}
(14) {{{4500 = 3*1500}}}
(15) {{{4500 = 4500}}}
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(3) {{{a + f + g = 6750}}}
(16) {{{4500 + 750 + 1500 = 6750}}}
(17) {{{6750 = 6750}}}
OK