How does one restate this mathematically?

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=98x + y = 98. Does one state the second equation as x/2=yzx/2 = y - z? But then wouldn't that add another variable?

Thank you.

Note by Michael David Sy
5 years, 11 months ago

No vote yet
3 votes

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

I 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, yy and the difference between their ages, aa

Then the man's current age is y+ay+a

When the man was as old as his wife is today, he was yy years old and his wife was yay - a

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

Hence the two equations.

Sameer Jain - 5 years, 11 months ago

Log in to reply

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

Michael David Sy - 5 years, 11 months ago

Log in to reply

Yes, but that will lead to aa being the second variable and not xx One equation will bey+a=2(y1) y + a = 2(y-1) The second is y+(y+a)=98y + (y + a) = 98

Sameer Jain - 5 years, 11 months ago

Log in to reply

@Sameer Jain Thanks. It really confused me. :)

Michael David Sy - 5 years, 10 months ago

Log in to reply

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

Michael Tang - 5 years, 11 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...