Question

The sum of two positive integers, x and y, is not more than 40. The difference of the two integers is at least 20. Chaneece chooses x as the larger number and uses the inequalities y ≤ 40 – x and y ≤ x – 20 to determine the possible solutions. She determines that x must be between 0 and 10 and y must be between 20 and 40. Determine if Chaneece found the correct solution. If not, state the correct solution.
Help Please!

Answer 1

Hi let me see

Answer 2

Thank you!

Answer 3

@Directrix can you help? I don't want to give a wrong answer :)

Answer 4

Do you want me to give you the possible answers?

Answer 5

Not to rush... but the quiz is timed..:)

Answer 6

@cnheawingspankk1 When you read this, read it slowly and make everything into symbols as you go. I'll help you get started by looking at this statement:
"The sum of two positive integers, x and y, is not more than 40."

So let's begin!

"The sum" This means we're adding right? So write a + sign down and find out what two things are adding when you read.

\[\Large +\]
" of two positive integers" Ok, so we know we're adding two positive integers, simple enough so far, but what are they?

"x and y" Ahhh, ok so we have the sum of x and y. So we put the "x" and "y" on either side of our "+" sign.
\[\Large x +y\]

"is not more than 40" Ok, so if it's not greater than 40, what sign is that? Well if it's not greater than 40 it can still be less than or equal to 40 right? So the symbol we can use is the less than or equal to sign.
\[\Large x +y \le 40\]

As an extra aside, we can also write this in case we think it's useful to us since we know they are positive: \[\Large x > 0 \\ \Large y > 0\]

Ok try to do this with the next sentence as best as you can, don't worry about getting it right just as long as you're trying.

Answer 7

Thank you so much!