Question

15) Ellie is six years older than Maisy. Zoe istwice as old as Ellie. The sum of their ages is50. How old is Zoe?

Answer 1

EXPLANATION

Assuming that x represents the age of Ellie, y represents the age of Maisy and z represents the age of Zoe, we can apply the following relationships:

x + y + z = 50 (1)

x = 6 + y (2)

z = 2x (3)

We have a system of three equations with three variables, thus we can compute the system as follows:

`\mathrm{Substitute\: }z=2x`
`\begin{bmatrix}x=6+y \\ x+y+2x=50\end{bmatrix}`
`Simplify\text{ }x+y+2x=50`

Grouping like terms:

`3x\text{ + y = 50}`

Now, we have:

`\begin{bmatrix}x=6+y \\ 3x+y=50\end{bmatrix}`
`\mathrm{Substitute\: }x=6+y`
`\begin{bmatrix}3\mleft(6+y\mright)+y=50\end{bmatrix}`

Applying the distributive property:

`\begin{bmatrix}18+4y=50\end{bmatrix}`
`\mathrm{Subtract\: }18\mathrm{\: from\: both\: sides}`
`18+4y-18=50-18`
`Simplify\colon`
`4y=32`
`\mathrm{Divide\: both\: sides\: by\: }4`
`(4y)/(4)=(32)/(4)`
`Simplify\colon`
`y=8`
`\mathrm{For\: }x=6+y`
`\mathrm{Substitute\: }y=8`
`x=6+8`
`Simplify\colon`
`x=14`
`\mathrm{For\: }z=2x`
`\mathrm{Substitute\: }x=14,\: y=8`
`z=2\cdot\: 14`
`\mathrm{Simplify}`
`z=28`
`\mathrm{The\: solutions\: to\: the\: system\: of\: equations\: are\colon}`
`x=14,\: z=28,\: y=8`

In conclusion, the age of Zoe is 28 years old.