SOLUTION: Randall is 75 years younger than karissa. 9 years ago karissas age was 4 times Randall’s age. How old is Randall now?

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Question 1166098: Randall is 75 years younger than karissa. 9 years ago karissas age was 4 times Randall’s age. How old is Randall now?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The site has so many of these. Students should be able to find a gigantic number of them already solved.



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PersonOne is n years younger than personTwo. p years ago, personTwo's age was k times personOnes age. How old is each person now?
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x, age of personOne
y, age of personTwo

system%28x=y-n%2Cy-p=k%28x-p%29%29

Substituting x from first equation into the second equation
y-p=k%28y-n-p%29
y-p=ky-kn-kp
ky-kn-kp=y-p
ky-y=-p%2Bkn%2Bkp
y%28k-1%29=kn%2Bkp-p
highlight%28y=%28kn%2Bkp-p%29%2F%28k-1%29%29-----------personTwo's age

Now to FIND for x
Use y=x%2Bn; substitute.
x%2Bn-p=k%28x-p%29
x%2Bn-p=kx-kp
n-p=kx-kp-x
n-p%2Bkp=kx-x
n-p%2Bkp=%28k-1%29x
highlight%28x=%28n-p%2Bkp%29%2F%28k-1%29%29------------personOne's age

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Randall is 75 years younger than karissa. 9 years ago karissas age was 4 times Randall’s age. How old is Randall now? 
Let Randall's age be R

Then Karissa's is: R + 75

We then get: R + 75 - 9 = 4(R - 9)

R + 66 = 4R - 36

R - 4R = - 36 - 66

- 3R = - 102

Randall or