Four years ago peter was three times as old as sylvia, and in 5 years the sum of their ages will be 38 years. find their present ages

peter is 19 and Sylvia is 9

Step-by-step explanation:

lets say p= Peter

and s=Sylvia

4 years ago, the equation is p-4= 3(s-4) because peter was 3 times older than sylvia 4 years ago which is why you have to multiply sylvia's current age by 3

when you simplify the equation you're left with p-4= 3s-12

when you solve for p, it equals 3s-8 (p=3s-8)

you substitute that as peter's age so you can end up with the same variable.

in 5 years the equation would be p+5+s+5=39 but since you need the same variable, you insert p=3s-8 as peter's age.

then you get the equation, 3s-8+5+s+5=38

when you simplify that you get, 4s+2=38

solve for s and you get 9 (s=9)

that means Sylvia is 9 years old

but we still need to find peter's age

you can choose to use either one of the equations to find out peter's age since you now know sylvia's

4 years ago:

9-4=5 subtract from sylvia's current age

5*3=15 because peter is 3 times older back then

15+4=19 because you need to find his current age

3

step-by-step explanation: