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# Writing two-variable inequalities word problem

Sal solves a word problem about scores in a chess tournament by creating a two-variable linear inequality.

## Want to join the conversation?

• I knew that there would eventually be a chess question, but I didn't think it would mention Fabi. Magnus Carlsen, Levon Aronian, and Hikaru Nakamura better be used too. : )
• What if the question also stated, that the maximum amount of games Fabiano can play is 10?
Would we then need to make a system of equations:
W + 1/2D ≥ 6.5
W + D = 10
And if that's the case, how would we solve this system?
(1 vote)
• If you say max of 10 games, then it would be W+D≤10. The issue with this is that you would actually have to consider 3 variables, (wins, draws, losses), so graphing in 3 dimensions is probably out of the question, thus you have to consider all possible answers. With 7 or more wins, it is obviously true. This would lead to multiple choices (10,0,0)(9,0,0)(9,1,0)(9,0,1)(8,0,0)(8,1,0)(8,1,1)(8,2,0)(8,0,1)(8,0,2), (7,0,0)(7,1,0)(7,1,1)(7,1,2)(7,2,0)(7,2,1)(7,3,0)(7,0,1)(7,0,2)(7,0,3). With 6 wins, it would require at least one draw giving (6,1,0)(6,1,1)(6,1,2)(6,1,3)(6,2,0)(6,2,1)(6,2,2)(6,3,0)(6,3,1) and (6,4,0). With 5 wins, you need at least 3 draws giving points (5,3,0)(5,3,1)(5,3,2)(5,4,0)(5,4,1) and (5,5,0). 4 wins require at least 5 draws giving (4,5,0)(4,5,1) and (4,6,0). 3 wins and 7 draws give (3,7,0) You have to win at least 3 total games.
These are related to triangular numbers with a pattern of 1, 3, 6, 10. Total number of choices would be starting from 10 wins and going down to 3, 1+3+6+10+10+6+3+1=40 possible solutions.
• I don't understand why we swap a sign when dividing both side by negative value? I know this is a rule but how I can derive it?
• By trial and error: If -x≥5, 0 does not work (0≥5), 5 does not work (-5≥5), but -5 does work (-(-5)≥5), -4 does not work (-(-4))≥5 or 4≥4), -6 and more will all work, so x≤-5.
Second way, if -x≥5, I can add x to both sides to get 0≥x+5, subtract 5 to get -5≥x. Flipping this around gives -x≤-5.
• yeah nice shoutout to Fabi!!
• This didn't help me with my problem.
Stacy's mom is baking treats for Stacy's birthday party. She has 9 eggs to use for this purpose. A batch of cookies requires 1 egg and a batch of brownies requires 2 eggs.
Write an inequality and shade the area to represent the solution.

Im stumped!
• Let cookies be on the y axis and brownies be on the x. The maximum number of cookie batches is 9, so graph (0,9), the theoretical maximum for brownies is 4.5, so plot (4.5,0) - I say theoretically because the most brownie batches will be 4. Connect these two points, and put dots on any pair of whole numbers below this line. While shading can be done, it is hard to assume that you could make partial batches rather than whole batches and I would also assume you are going to use as many eggs as possible.
• So, if he gets 1/2 point for a draw, why is it written 0.5d? Would one draw give him the half point he needs?

Why isn't the inequality written W+D≥6.5?
• If you use your version of the inequality, it means that every draw is worth 1 point, not 1/2. So, you would get the wrong results.
• How do I help my daughter with this: Suppose s and t are two numbers and that s>t. Determine whether each inequality must be true.
A. s + 15 > t + 15
• If s is always Greater Than (>) t, than we can use that info to plug in for those two, so let's use s=6 and t=5, so 6 > 5. (6) + 15 > (5) + 15, so it is true.
• Is there any solution for -b <( x-y)b<b?
Or
How to solve it?