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johnnyzxz
Registered User Posts: **494** Member

I'm begging you. Please don't answer if you're not gonna explain step by step.

I'm lost in the world of inequalities. It is my ultimate weakness.

Please, assume I am a 7th grader and that I've recently been introduced to inequalities.. lol

t^2 - k^2 < 6

t + k > 4

If t and k are positive integers, and t > k , what is the value of t?

I'm lost in the world of inequalities. It is my ultimate weakness.

Please, assume I am a 7th grader and that I've recently been introduced to inequalities.. lol

t^2 - k^2 < 6

t + k > 4

If t and k are positive integers, and t > k , what is the value of t?

Post edited by johnnyzxz on

This discussion has been closed.

## Replies to: Math question DONT ANSWER IF YOU DONT WANT TO EXPLAIN

261Junior Member(t^2 - k^2) = (t + k)(t - k) - just an application of the theorem to our problem;

(t + k) must be greater than 4, so let's just make it 5;

(5)(t - k) = (t^2 - k^2), which must be something less than 6, let's call it 5 too.

(5)(t - k) = 5 - simplify those fives out.

(t - k) = 1 - you have an equation! t is one greater than k.

t = 1 + k;

t = 3; k = 2; I think that fulfills both conditions.

1,071Senior MemberBut if you want to know WHY 3 and 2 are the only numbers that work...since we are limited to integers, look at the squares of consecutive integers. After 2^2 and 3^2, you will see that the squares of consecutive integers all differ by more than 6. So when they said that t + k >4, they guaranteed that 2 and 3 were the only pair that you could use.

But if that last paragraph didn't make sense, it really doesn't matter. I tell students all the time: play with numbers, find numbers that work and then go with them.

261Junior MemberCase in point, when I was solving that, I had no idea where I was actually doing, and ultimately came to the equation t = 1 + k. From there, I tried a few random values and came to the conclusion that both conditions are satisfied when t = 3. If both conditions are satisfied and there's no glaring caveat, you have arrived at the correct answer!

1,071Senior Member494MemberI truly appreciate your answers, but I still don't feel comfortable with this question. Is the only way to answer it really just putting in random numbers? I would have no idea where to start, and it would end up taking a minute just like this did..

Could someone please explain this by mostly using inequalities and substituting the least amount possible?

P.S. the answer is t = 3

3New Memberhttp://wildaboutmath.com/2012/03/22/an-sat-math-problem-with-logic-algebra-and-inequalities/