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.

 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.

Step-by-step 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.