Question

8. Olivia's brother is twice her age

Answer 1

The ages of Olivia and her brother are 10 years and 11 years respectively

Let x₁, and x₂ be the ages of Olivia and her brother respectively.

Given that Olivia's brother is twice her age minus 9 years.

⇒ x₂ = 2x₁ - 9 → equation 1

Also given that Olivia's brother is as old as half the sum of the ages of Olivia and both of her 12-year-old twin brothers.

⇒ x₂ = 1/2 × (x₁ + 12) → equation 2

Using equation 1 in equation 2, we get

2x₁ - 9 = 1/2 × (x₁ + 12)

⇒ 4x₁ - 18 = x₁ + 12 (multiplying by 2 on both sides)

⇒ 4x₁ - x₁ = 12 + 18

⇒ 3x₁ = 30

⇒ x₁ = 10 (dividing by 3 on both sides)

Using the value of x₁, in equation 1,

⇒ x₂ = 2(10) - 9

⇒ x₂ = 20 - 9

⇒ x₂ = 11

Therefore the ages of Olivia and her brother are 10 years and 11 years respectively.

Learn more at:

brainly.com/question/28016937

brainly.com/question/28016937

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