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.