Question

Rebecca is x years old.

Mary is 8 years older than Rebecca. Jill is three times older than Mary. The sum of their ages is 67.
(a) Form an equation in terms of x
(b) Solve the equation and work out Rebecca’s, Mary’s and Jill’s ages.

Answer 1

Given that Rebecca is x years old and Mary is 8 yrs older than her , so the age of Mary will be;

`\longrightarrow Age_(Mary)= x+8`

Again Jim is 3 times older than Mary, so the age of Jim will be,

`\longrightarrow Age_(Jim)= 3(x+8)`

Now we are given that the sum of their ages is 67. So that ;

Equation in terms of x :-

`\longrightarrow x + (x+8) +3(x+8)=67`

Solving the equation,

`\longrightarrow x + x +8+3x+24=67\\`

`\longrightarrow 5x + 32 =67\\`

`\longrightarrow 5x = 67-32 \\`

`\longrightarrow 5x = 35\\`

`\longrightarrow x = 7`

So ,

• Age of Rebecca= x = 7 yrs
• Age of Mary = x+8 = 15yrs
• Age of Jim =3(x+8) = 45 yrs .

And we are done!