SOLUTION: This question was in my daughters Year 8 maths test today and I am of no help A father observes that the ratio of his age to his daughters age is 3:2 right now. But his daughter

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Question 1035904: This question was in my daughters Year 8 maths test today and I am of no help
A father observes that the ratio of his age to his daughters age is 3:2 right now. But his daughter observes that in 8 years time their ages will be 7:5
Is this enough information to determine their ages?
If Yes, what are their ages
If No, explain why
Thanks for your help
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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%28system%28y%2Fx=3%2F2%2C%28y%2B8%29%2F%28x%2B8%29=7%2F5%29%29

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 can be solved. Let us try some arithmetic or algebra steps.

Try using multiplicative inverse property.

-
system%28y=3x%2F2%2C5%28y%2B8%29=%28x%2B8%29%2A7%29
-
Simplify the second equation.
system%28y=3x%2F2%2C5y%2B40=7x%2B56%29
-
Substitute for y into the second equation.
5%283x%2F2%29%2B40=7x%2B56
continue algebraic steps, not saying the names of the properties being used (hopefully they are not needed to be identified...)
15x%2F2%2B40=7x%2B56
15x%2B80=14x%2B112
15x-14x%2B80=112
x%2B80=112
x=112-80
highlight%28x=32%29--------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%2832%29%2F2
y=%283%2A32%29%2F2
y=%283%2A2%2A16%29%2F2
y=3%2A16
highlight%28y=48%29-------------result for father's age now.