Question 414342
Let {{{a}}} = amount received by each friend
Let {{{b}}} = amount received by each charity
Let {{{c}}} = amount received by the University
given:
(1) {{{5a + 4b + c = 975240}}}
(2) {{{a = 3*4*b }}}  
(3) {{{b = 2c}}}
This is 3 equations and 3 unknowns, so it's solvable
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Substitute (3) into (1)
(3) {{{c = (1/2)*b}}}
(1) {{{5a + 4b + (1/2)*b = 975240}}}
Substitute (2) into (1)
(1) {{{5*12*b + 4b + (1/2)*b = 975240}}}
{{{60b + 4b + (1/2)*b = 975240}}}
{{{128b + b = 1950480}}}
{{{b = 1950480/129}}}
{{{b = 15120}}}
and
(3) {{{c = (1/2)*15120}}}
{{{c = 7560}}}
and
(2) {{{a = 12b }}}
{{{a = 12*15120}}}
{{{a = 181440}}}
The 5 friends each got $181,440
The 4 charities each got $15,120
The University got $7,560
check answer:
(1) {{{5a + 4b + c = 975240}}}
(1) {{{5*181440 + 4*15120 + 7560 = 975240}}} 
(1) {{{907200 + 60480 + 7560 = 975240}}}
(1) {{{975240 = 975240}}}
OK