Question 698308
The problem should be
“Alice is 8/3 as old as her daughter.
In 4 years, Alice will be 9/4 as old as her daughter.
Find their ages”
{{{x}}} = Alice's age
{{{y}}} = the daughter's age
{{{x=(8/3)y}}} because Alice is 8/3 as old as her daughter.
{{{x=(8/3)y}}} --> {{{3x=8y}}} --> {{{3x-8y=0}}}
In 4 years, Alice will be {{{x+4}}},
her daughter will be {{{y+4}}},
and their ages will be related by the equation
{{{x+4=(9/4)(y+4)}}} --> {{{4(x+4)=9(y+4)}}} --> {{{4x+16=9y+36}}} --> {{{4x-9y=36-16}}} --> {{{4x-9y=20}}}
 
We get the system
{{{system(3x-8y=0,4x-9y=20)}}}
Multiplying the first equation times {{{(-4)}}} and the second times {{{3}}} we get
{{{system(-12x+32y=0,12x-27y=60)}}} , and adding both equations we get
{{{5y=60}}} --> {{{y=60/5}}} --> {{{highlight(y=12)}}}
Substituting into {{{3x=8y}}} we get
{{{3x=8*12}}} --> {{{3x=96}}} --> {{{x=96/3}}} --> {{{highlight(x=32)}}}