Question

Ellie is six years older than Maisie Zoe is twice as old as Eli. The sum of their ages is 50. How old is Zoe?

Answer 1

Let the age of Maisie be x

From the first statement, Ellie is six years older than Maisie implying:

`\text{Ellie's age = x + 6}`

From the second statement, Zoe is twice as old as Eli implying:

`\text{Zoe's age = 2(x+6)}`

From the last statement, the sum of their ages is 50 implying:

`x\text{ + x + 6 + }2(x\text{ + 6) = 50}`

Solving for x:

We open the bracket and collect like terms

`\begin{gathered} x+x\text{ + }6\text{ + 2x + 12 = 50} \\ x\text{ + x + 2x + 6 + 12 = 50} \\ 4x\text{ + 18 = 50} \\ 4x\text{ = 50 - 18} \\ 4x\text{ = 32 } \\ \text{Divide both sides by 4} \\ (4x)/(4)\text{ = }(32)/(4) \\ x\text{ = 8} \end{gathered}`

Hence, Zoe's age is:

`\begin{gathered} =2(x\text{ + 6)} \\ =\text{ 2(8+6)} \\ =\text{ 2 }*\text{ 14} \\ =\text{ 28} \end{gathered}`

Answer:

Zoe's age = 28