This isn't my homework. It's a math problem I picked up while reading a book to promote clearer thinking. I know the answers are 56 and 42, but I'm wondering about how to restate the second equation in the system with this problem: 'the ages of a man and his wife together are 98. He is twice as old as she was when he was the age she is today. What are their ages?'

Obviously, the first equation would be \[x + y = 98\]. Does one state the second equation as \[x/2 = y - z\]? But then wouldn't that add another variable?

Thank you.

No vote yet

3 votes

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestI suppose you meant to say "He is as old as 's'he was ...."

You can take the variables as the current age of the wife, \(y \)and the difference between their ages, \(a\)

Then the man's current age is \(y+a\)

When the man was as old as his wife is today, he was \(y\) years old and his wife was \(y - a\)

We are given that \(y +a = 2(y - a) \)

Hence the two equations.

Log in to reply

That still creates a third equation, because a is not known. Thank you! :)

Log in to reply

Yes, but that will lead to \(a\) being the second variable and not \(x\) One equation will be\( y + a = 2(y-1)\) The second is \(y + (y + a) = 98\)

Log in to reply

Log in to reply

?? Wouldn't the second EQ just be \(x = 2y?\)

Log in to reply