Question

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

Answer 1

P = age of Peter and S = Sylvia's age. We will first decipher "four years prior Peter was three times as old as Sylvia." This can be composed P = 4 + 3*(S-4). Next, we interpret "in 5 years the total of their ages will be 38 years" as (P + 5) + (S + 5) = 38. Presently we have two questions (P and S) and two conditions, so we are prepared to settle. We substitute our first condition for P into our second condition: (4+3*(S-4)+5) + (S+5) = 38 9 + 3S - 12 + S + 5 = 38 2 + 4S = 38 4S = 36 S = 9. Substitute this once more into the main condition to discover P = 4+3*(S-4) = 4+3*(9-4) = 4+15 = 19.

Answer 2

Answer: peter is 19 and Sylvia is 9

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