Wina is five years younger than Gwen. Gwen is ten years younger than Berth.How old is each if the sum of their ages is 39.

Question

Pls. do explain the anser.

Answer 1

I will use G = Gwen's age, B = Berth, and W = Wina.

G + B + W = 39 (sum of ages is 39)

Wina is (W =) 5 years younger than Gwen (G - 5). So, W = G - 5

Gwen is (G =) 10 years younger than Berth (B - 10). So, G = B - 10 or B = G + 10

G + (G + 10) + (G - 5) = 39 by substituting equivalent expressions of age from above statements.

3G + 5 = 39 from simplifying by combining like terms

3G = 34 subtract 5 from each side

G = 34/3 years. This is readily identified as Gwen's age!

W = G - 5 = 34/3 - 5 = 34/3 - 15/3 = 19/3 years (convert 5 to 15/3) This is readily identified as Wina's age.

B = G + 10 = 34/3 + 10 34/3 + 30/3 = 64/3 years (convert 10 to 30/3) This is readily identified as Berth's age.

Answer 2

Let x be Bertha's age. If Gwen is 10 yrs younger than Bertha, then Gwen is x -10. Wina is 5 years younger than Gwen: Wina = Gwen - 5, but Gwen is x-10, so Wina = (x - 10) - 5 or x - 15.

Summing all three, you get x + x -10 + x - 15 = 39

3x - 25 = 39 -> 3x = 64 -> x = 64/3 = 21 1/3 yrs old (a strange result, but it checks!)

Check: Bertha 21 1/3 + Gwen 11 1/3 + Wina 6 1/3 = 38 3/3 = 39 yrs total.