Question

5. Paul is x years old.

Rebecca is four times older than Paul.
Gemma is 10 years older than Paul.
the sum of their ages is 82 Years.
(a) Form a simplified equation in terms of x
(b) Solve the equation and work out each persons age.

Answer 1

Answer: A) The equation will be x + 4x + x + 10 = 82 B) Paul's age is 12, Rebecca's age is 48 and Gemma's age is 22.

Explanation:

We will represent Paul's age by the equation p= x where p is Paul

We will represent Rebecca's age by the equation r = 4x Where r is Rebecca

We will represent Gemma's age by the equation g = x + 10 where g is also Gemma's age.

We given that the sum of their ages is 82 years so meaning that x + 4x + x + 10 has to equal 82.

A) The equation will be x + 4x + x + 10 = 82

Solve for the x equation to find Paul age because his age is x.

B) (x) + (4x) + (x+10) = 82 combine like terms on the left side

6x + 10 = 82

-10 -10

6x = 72

x= 12

Paul age is 12.

r= 4(12)

r = 48

Rebecca's age is 48.

g= 12 +10

g= 22

Gemma's age is 22.