CalculatorUser

I feel so jealous! Here in Illinois, nothing happens! Everybody in my class gets EXCITED if there is a THUNDERSTORM! It's so boring here the weather is ALWAYS cloudy and the air is cold.

California seems like such an exciting place, that's why a lot of my friends dream of going to California lol.

A lot of people in our class actually WANT earthquakes and tornadoes because nothing EVER happens.

im so young i still play video games and have playdates XD like, actually.

You guys are old, im GOING into 8th grade

Whenever you have an equation in this form, try to isolate x, then take the square roots of both sides

This is called the square roots method.

Thank you Heureka! That is a very elegant solution, this problem was so hard all my friends were stumped.

When you thought the answer is 2, this was your mistake:

You thought \(\Delta\) could be a two digit number, and assumed it was 12.

However, in the problem, it states "1\(\Delta\)". It cannot be "112"

So in the future, be careful, remember that when "1\(\Delta\)" happens, \(\Delta\) must be SINGLE digit number.

You read it wrong!!! Oops!

It said difference, not sum

This is my way, there might be a better way.

When it says "their product is 45" I just find its factor pairs

5 * 9

15 * 3

Those are the first to come into my mind

Then I instantly recognize 15 and 3 has a DIFFERENCE of 12.

You can make a system of equations, but that is too slow.

Notice how -7 is a prime numbers

That means -7 has only two factors!

They are 1 and -7, OR it can be -1 and 7.

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The second phrase you said is that the two numbers add up to 6.

So considering the two cases above, which of them add up to 6?

You can always make an equation, but the fastest way to this is recognize that 7 is prime.

I don't really have a good method, but this is what I did:
 

notice x*y*z = 54

So prime factorize 54

3 * 3 * 3 * 2

Ok so with the prime factorization, it isn't tedious at all to guess and check with those numbers into the other equations.

x + y - z = 0 (the first equation) is also:

x + y = z

and

xyz = 54

It is much easier now to guess and check with only the prime factorization.

The second equation is very complicated we can use it to check our three x, y, and z values later.

So with our prime factorization 3 * 3 * 3 * 2

I guessed that (3, 3, 6) is a solution to the equations we have above. Then we check with the second equation to make sure it is true, which it is.

Ok, notice how our answer also could be negative. However, that can't be true because xyz = 54 has to have two negative numbers but the only solution to x + y = z has three.

So the answer is 1 I believe...

This problem was more of a logic puzzle with guessing in my opinion.

Just curious, what are you learning currently? Because this teacher gave you something that doesn't seem to fit into any curriculum...