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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.
• Why isn't the inequality (W + D ≥ 6.5)? The sentence states that .5 = "points for each game that ends in a draw", which = D. Isn't saying .5D being redundant?
(1 vote)
• D doesn't equal 0.5 points automatically so you would need a coefficient. D is just a variable so we can't assume that it has value.
(1 vote)
• 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.
• how to do this
• 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.
• 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.
• Is there any solution for -b <( x-y)b<b?
Or
How to solve it?
• Please clarify - You have multiple variables. What variable were you asked to solve for?

Note: With 3 variables and 1 inequality, you can't get to a numeric answer. You don't have enough info.
(1 vote)
• 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!