.Solve the Algebra 1 Puzzle: Two Men and Their Ages

In summary, the two men were discussing their ages and the difference between them. The older man said he was 94 years old and the younger said he was 85 years old. The older man said that the sum of their ages and his plus the difference of the younger man's age multiplied by 8512 would be. The younger man said that x^2+94x-94x+8836 would be the answer. The older man said that x^2+8836 would be the answer after combining like terms. The older man said that x^2-324 would be the answer to simplify the -x^2 term. The younger man said that x^2-324 would be the answer to simplify the -x^2 term
  • #1
kai89
4
0
Algebra 1 Help!

This is really easy but I just can't seem to get it.

Two men were talking about their ages. One said he was 94 years old. "Then," said the younger, "the sum of your age and mine multiplied by the difference will be 8512." How old was the young man.

I thought all i had to do was solve for x
(94-x)(94+x)=8512 but i get a larger number I kept doing it over and over thinking it was a foil mistake but its still wrong. I'm thinking I am gettin tripped up at "multiplied by the difference" the difference of what? If anyone can help me it is greatly appreciated. Thanks
 
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  • #2
Your equation is correct. When you multiply out the brackets, you should arrive at an equation for x2. Perhaps you forgot to take the square root, that may be why you have got a large number. If this doesn't help, post your work and we may be able to spot a mistake, if there is one!
 
  • #3
Sorry, wrong place...
 
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  • #4
You might also fiddle about with the prime factorization 8512=2*2*2*2*2*2*7*19
 
  • #5
This is my first attempt with LaTeX.

As the others have said, your equation is correct.
[tex](94-x)(94+x)=8512[/tex]

After performing FOIL operation:

[tex]-x^2+94x-94x+8836=8512[/tex]

After combining like-terms:

[tex]-x^2+8836=8512[/tex]

To isolate the [tex]-x^2[/tex] term:

[tex]-x^2=-324[/tex]

Now, in order to simplify the [tex]-x^2[/tex] term, you must take the square root. I am not sure if you have come across radicals or not yet, but if the index (the root, [tex]n[/tex]) is even, then the radicand cannot be negative. You will end up with an irrational number.

This is in the form:
[tex](\sqrt[n]{a})^m[/tex]

In order to get rid of the negative sign:

[tex]+(-x^2=-324)[/tex]

Then:

[tex]\sqrt{x^2}=\sqrt{324}[/tex]

From here, see if you can complete the problem.
 
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  • #6
complexPHILOSOPHY said:
In order to get rid of the negative sign:

[tex]+(-x^2=-324)[/tex]

And, BTW, you would do this to get rid of the negative sign:

[tex]
-(-x^2=-324)
[/tex]

not this:

[tex]
+(-x^2=-324)
[/tex]
 
  • #7
I appreciate you've probably solved this problem by now, but there's an interesting thing with expressions like the one you're dealing with, which is one of the first things they teach us here in the UK when it comes to algebra:
An expression of the format (y+x)(y-x) expands to become y^2-x^2. So straight away, taking y as 94, you can get:

94^2-x^2=8512
>> x^2 = 94^2 - 8512
>> x^2 = 324

With simple problems it's often easy to expand the brackets manually, then re-factor once you have a quadratic in x. However, it can be useful and time - saving to learn to spot these little tricks.
 
  • #8
chuckd1356 said:
And, BTW, you would do this to get rid of the negative sign:

[tex]
-(-x^2=-324)
[/tex]

not this:

[tex]
+(-x^2=-324)
[/tex]

Sorry, I hit the wrong symbo on the keyboard.
 
  • #9
No problem, just making sure the kid didn't get confused.
 
  • #10
chuckd1356 said:
No problem, just making sure the kid didn't get confused.

I definitely appreciate it, as well my friend.
 

What is the Algebra 1 Puzzle: Two Men and Their Ages?

The Algebra 1 Puzzle: Two Men and Their Ages is a mathematical puzzle that involves using algebraic equations to determine the ages of two men based on a series of clues.

What are the basic steps to solve the puzzle?

The basic steps to solve the puzzle are:

  1. Read and understand the clues given in the puzzle.
  2. Assign variables for the unknown ages of the two men.
  3. Write algebraic equations based on the clues.
  4. Solve the equations to find the values of the variables.
  5. Check if the solution satisfies all the given clues.

What are some helpful tips for solving the puzzle?

Some helpful tips for solving the puzzle are:

  1. Start by assigning variables for the unknown ages.
  2. Use the clues to create equations and eliminate unnecessary information.
  3. Simplify the equations by combining like terms or using inverse operations.
  4. Be organized and keep track of your work.
  5. Double check your solution to make sure it satisfies all the given clues.

What skills are required to solve the puzzle?

To solve the Algebra 1 Puzzle: Two Men and Their Ages, you will need to have a good understanding of basic algebraic concepts such as variables, equations, and solving equations. You will also need critical thinking and analytical skills to interpret the clues and come up with a logical solution.

Is there a specific method to solve the puzzle?

There is no specific method to solve the puzzle, as different people may approach it in different ways. However, the basic steps mentioned earlier (reading the clues, assigning variables, writing equations, solving and checking) are commonly used by many people to solve the puzzle.

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