Question 1173031
Five years ago Barbra was four-fifths Bill's age then. In ten years she will be
seven-eights his age then.
<pre>
You omitted the question which obviously was "How old are they now?"  Ikleyn
gets all bent outta shape when students leave out anything.  I don't.  But
instead of doing your problem for you, I'll do one exactly like it step-by-
step.  Here is the problem I will do for you:
</pre>Seven years ago Barbra was two-thirds Bill's age then. In four years she will
be three-fourths his age then.  How old are they now?<pre>
Let x = Barbra's age now
Let y = Bill's age now
Then x-7 = Barbra's age 7 years ago
Then y-7 = Bill's age 7 years ago
Also x+4 = Barbra's age 4 years from now
Also y+4 = Bill's age 4 years from now
</pre>Seven years ago Barbra was two-thirds Bill's age then.<pre>

{{{x-7 = expr(2/3)(y-7)}}}
</pre>In four years she will be three-fourths his age then.<pre> 

{{{x+4 = expr(3/4)(x+4)}}}

The system you are to solve is

{{{system(x-7 = expr(2/3)(y-7),x+4 = expr(3/4)(y+4))}}}

Multiply the first equation through by 3 and the second one through by 4 to
clear the fractions:

{{{system(3x-21 = 2(y-7),4x+16 = 3(y+4))}}}

Distribute the right sides:

{{{system(3x-21 = 2y-14,4x+16 = 3y+12)}}}

Rearrange the terms:

{{{system(3x-2y=7,4x-3y=-4)}}}

To eliminate y, multiply the first equation by -3 and the second equation by 2:

{{{system(-9x+6y=-21,8x-6y=-8)}}}

Add term-by-term to eliminate the y-terms

{{{-x=-29}}}
{{{x=29}}}, So Barbra is 29    

Substitute in 

{{{3x-2y=7)}}}
{{{3(29)-2y=7)}}}
{{{87-2y=7}}}
{{{-2y=-80}}}
{{{y=40}}}, so Bill is 40.

Checking:
Seven years ago Barbra was 29-7=22
Seven years ago Bill was 40-7=33
Indeed, 22 is 2/3 of 33.  That checks.

In four years, Barbra will be 29+4=33
In four years, Bill will be 40+4=44
Indeed, 33 is 3/4 of 44.  That checks.

Now do your problem the exact same way step by step, using this as a guide.

Edwin</pre>