Question 1035904
Grade 8 level exercise, not sure.  Variables would be helpful.


y for Father's age now.
x for daughter's age now.


Transcribe or translate the description, literally.
{{{highlight_green(system(y/x=3/2,(y+8)/(x+8)=7/5))}}}


This is a system of two of what really are LINEAR equations in two unknown variables.
If your daughter is in a Pre-Algebra course, maybe she will understand this discussion just
given, and could solve the system of equations. 



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REVIEWING WHAT WAS JUST POSTED:


(1)
Assigned variables for the current ages of Father and his Daughter

(2)
Translated the description of the problem into equations

(3)
Need to SOLVE the system of equations  (not yet shown)



You want to solve the system of equations and to know if in fact, the system <i>can</i> be solved.  Let us try some arithmetic or algebra steps.


Try using multiplicative inverse property.
{{{system(x(y/x)=x(3/2),(5(x+8))((y+8)/(x+8))=(5(x+8))(7/5))}}}
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{{{system(y=3x/2,5(y+8)=(x+8)*7)}}}
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Simplify the second equation.
{{{system(y=3x/2,5y+40=7x+56)}}}
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Substitute for y into the second equation.
{{{5(3x/2)+40=7x+56}}}
continue algebraic steps, not saying the names of the properties being used (hopefully they are not needed to be identified...)
{{{15x/2+40=7x+56}}}
{{{15x+80=14x+112}}}
{{{15x-14x+80=112}}}
{{{x+80=112}}}
{{{x=112-80}}}
{{{highlight(x=32)}}}--------one of the results, the daughter's age now.


Use the first equation found before the system was simplified, being y=3x/2 and evaluate y, knowing the found value for x:
{{{y=3(32)/2}}}
{{{y=(3*32)/2}}}
{{{y=(3*2*16)/2}}}
{{{y=3*16}}}
{{{highlight(y=48)}}}-------------result for father's age now.