Question 130046
{{{a}}}= number of 10 oz cups
{{{b}}}= number of 14 oz cups
{{{c}}}= number of 20 oz cups
{{{105a + 135b + 165c = 4500}}}
{{{21a + 27b + 33c = 900}}}
(1) {{{7a + 9b + 11c = 300}}}
(2) {{{a + b + c = 34}}}
(3) {{{10a + 14b + 20c = 5*96}}}
From (2):
(4) {{{c = 34 - a - b}}}
Substitute this in (1)
(1) {{{7a + 9b + 11c = 300}}}
{{{7a + 9b + 11*(34 - a - b) = 300}}}
{{{7a + 9b + 374 - 11a - 11b = 300}}}
{{{-4a - 2b = - 74}}}
{{{2a + b = 37}}}
(5) {{{b = 37 - 2a}}}
Substitute (4) and (5) in (3)
(3) {{{10a + 14b + 20c = 5*96}}}
{{{10a + 14*(37 - 2a) + 20*(34 - a - b) = 5*96}}}
{{{10a + 518 - 28a + 680 - 20a - 20b) = 5*96}}}
{{{-38a - 20b = 480 - 518 - 680}}}
{{{38a + 20b = 718}}}
substitute (5) for {{{b}}}
{{{38a + 20*(37 - 2a)  = 718}}}
{{{38a + 740 - 40a = 718}}}
{{{-2a = -22}}}
{{{a = 11}}}
(5) {{{b = 37 - 2a}}}
{{{b = 37 - 2*11}}}
{{{b = 15}}}
(4) {{{c = 34 - a - b}}}
{{{c = 34 - 11 - 15}}}
{{{c = 8}}}
Keith filled {{{11}}} 10 oz cups, {{{15}}}14 oz cups,
and {{{8}}} 20 oz cups
check answer:
(1) {{{7a + 9b + 11c = 300}}}
{{{7*11 + 9*15 + 11*8 = 300}}}
{{{77 + 135 + 88 = 300}}}
{{{300 = 300}}}
(2) {{{a + b + c = 34}}}
{{{11 + 15 + 8 = 34}}}
{{{34 = 34}}}
(3) {{{10a + 14b + 20c = 5*96}}}
{{{10*11 + 14*15 + 20*8 = 480}}}
{{{110 + 210 + 160 = 480}}}
{{{480 = 480}}}
OK