Question 227707
Let {{{j}}}= cost of a carton of juice
Let {{{f}}}= cost of a fruit cup
Let {{{s}}}= cost of a bowl of soup
given:
(1) {{{9j = 5f}}}
(2) {{{f = s + 50}}} (in cents)
(3) {{{s = j + 50}}} (in cents)
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Rewrite equations
(1) {{{j = (5/9)*f}}}
(2) {{{f - s = 50}}}
(3) {{{-j + s = 50}}}
Add (2) and (3)
{{{f - j = 100}}}
Substitute (1) in this equation
{{{f - (5/9)*f = 100}}}
{{{(4/9)*f = 100}}}
{{{4f = 900}}}
{{{f = 225}}}
and, since
(2) {{{f - s = 50}}}
{{{225 - s = 50}}}
{{{s = 175}}}
And
(3) {{{-j + s = 50}}}
{{{-j + 175 = 50}}}
{{{j = 175 - 50}}}
{{{j = 125}}}
A carton of juice costs $1.25
A fruit cup costs $2.25
A bowl of soup costs $1.75
check:
{{{9j = 5f}}}
{{{9*125 = 5*225}}}
{{{1125 = 1125}}}
OK