Finding the younger man's age using sum and difference

[kai89]

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

 

[cristo]

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!

 

[disregardthat]

Sorry, wrong place...

 

[arildno]

You might also fiddle about with the prime factorization 8512=2*2*2*2*2*2*7*19

 

[complexPHILOSOPHY]

This is my first attempt with LaTeX.

As the others have said, your equation is correct.
$$(94-x)(94+x)=8512$$

After performing FOIL operation:

$$-x^2+94x-94x+8836=8512$$

After combining like-terms:

$$-x^2+8836=8512$$

To isolate the $$-x^2$$ term:

$$-x^2=-324$$

Now, in order to simplify the $$-x^2$$ 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, $$n$$) is even, then the radicand cannot be negative. You will end up with an irrational number.

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

In order to get rid of the negative sign:

$$+(-x^2=-324)$$

Then:

$$\sqrt{x^2}=\sqrt{324}$$

From here, see if you can complete the problem.

 

[chuckd1356]

In order to get rid of the negative sign:

$$+(-x^2=-324)$$

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

$$-(-x^2=-324)$$

not this:

$$+(-x^2=-324)$$

 

[weatherhead]

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.

 

[complexPHILOSOPHY]

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

$$-(-x^2=-324)$$

not this:

$$+(-x^2=-324)$$

Sorry, I hit the wrong symbo on the keyboard.

 

[chuckd1356]

No problem, just making sure the kid didn't get confused.

 

[complexPHILOSOPHY]

No problem, just making sure the kid didn't get confused.

I definitely appreciate it, as well my friend.