SOLUTION: One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. What is the present age of the father?

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Question 947686: One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. What is the present age of the father?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let man’s present age be x and son’s age y}

if one year ago, a man was 8 times as old as his son, then we have
x-1=8%28y-1%29 ...............eq.1 solve for x
x=8y-8%2B1
x=8y-7
Now his age is equal to the square of his son’s age:
x=y%5E2 ...............eq.2
go to
x=8y-7 ..........substitute in eq.2
8y-7=y%5E2 ...............eq.2..1 solve for y
0=y%5E2+-8y%2B7 ...factor
0=y%5E2+-y-7y%2B7
%28y%5E2+-y%29-%287y-7%29=0
y%28y+-1%29-7%28y-1%29=0
%28y+-7%29%28y-1%29=0
solutions:
if %28y+-7%29+=0 => highlight%28y=7%29
if %28y-1%29=0 => y=1 .........we can disregard y=1 because it will give us same present age for both, father and son
now find x
x=y%5E2 ...............eq.2
plug in y=7
x=7%5E2
highlight%28x=49%29
so, now father is highlight%2849%29 and son highlight%287%29
check:
year ago father is 48 and son 6, and a man was 8 times as old as his son which is true because 6%2A8=48