Question

Peter is x years old and his sister is 5 years older. If the product of their ages is 84, form an equation in x and solve it to find peter's age

Answer 1

x^2 + 5x - 84 = 0

x = 7

Explanation:

let the sister's age = y

sister's age (y) = 5 + x equation 1

xy = 84 equation 2

Make y the subject of the formula in equation 2

y = 84/x

equate equation 1 and 2

84/x = 5 + x equation 3

Multiply equation 3 by x

84 = 5x + x^2

x^2 + 5x - 84 = 0

tjis can be solved using quadratic equation

x^2 -7x + 12x -84 = 0

x(x + 12) -7(x + 12)

x = 7 or - 12

age cant be negative so his age is 7