Dad is 7 times as old as his son. 10 years later, he will be three times as old as his son. find their ages?

So dad is represented by x

son is represented by y

so x is (x=) 7 times his son (7y)

our first sentence is x=7y

10 years later (x+10, y+10) he will be 3 times as old as his son (x+10=3 (y+10))

or 10+x=3 (y+10)

so our sentences are

x=7y

and

x+10=3 (y+10)

first we subsitute x=7y for x in the second equation

(7y) + 10=3 (y+10)

7y+10=3 (y+10)

we distribute

7y+10=3y+30

subtract 3y from both sides

4y+10=30

subtract 10 from both sides

4y=20

divide both sides by 4

y=5

the son is currently 5 years old

x=7y

subsitute y=5 for y in equation

x=7 (5)

x=35

the dad is currently 35 years old

in 10 years

dad is 45 and son is 15

dad=35

son=5

These are the answers

son = 5

dad = 35