Katy's mother is one year older than three times Katy's age and the sum of their ages is 57.

Write an equation, using k to represent Katy's age in years.

Also solve the equation to find the value of k, show all your working out.

Let m = mother's age.

m = 3k + 1 (1)

m + k = 57 (2)

from (2) we have m = 57 - k. (3)

Replace the m in (1) using (3)

57 - k = 3k + 1

Subtract 1 from both sides

56 - k = 3k

Add k to both sides

56 = 4k

Divide both sides by 4

14 = k (or just k = 14)

.

Let Kathy's age = k, then we have:

The mother's age =3k + 1, but:

k + 3k + 1 = 57

4k =57 - 1

4k = 56 divide both sides by 4

k =56 / 4

k = 14 - Kathy's age, and 3*14 + 1 =43 - her mother's age.