Question

Zelda has two children: Adam and Elliot. Zelda is seven times as old as Adam, who is threeyears younger than Elliot. Next year, Zelda will be four times as old as Elliot. How old is Zelda?

Answer 1

Answer: e:9

Explanation:

Answer 2

Let
`z, a, e` be the ages of Zelda, Adam and Elliot, respectively.

Let's translate the given information into equations: Zelda is seven times as old as Adam means that
`z = 7a`

Adam is three years younger than Elliot means
`a = e-3`

Next year, Zelda will be four times as old as Elliot means
`z+1 = 4(e+1)`

So, you have the system

`\begin{cases} z = 7a\\a = e-3\\z+1 = 4(e+1)\end{cases}`

Use the first equation to express z in terms of a: the last two equations become

`\begin{cases} a = e-3\\7a+1 = 4(e+1)\end{cases}`

Use the first equation to express a in terms of e: the last equation becomes

`7(e-3)+1=4(e+1) \iff 7e-21+1=4e+4 \iff 3e = 24 \iff e=8`

So, Elliot is 8 years old. Adam is three years younger, so he is 5 years old. Zelda is seven times as old as Adam, so she is 35 years old.