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# Graphs of two-variable inequalities word problem

Given the graph of a two-variable linear inequality that models a context about dog biscuits, Sal finds if the dog can get enough biscuits.

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• How is she fulfilling her if she wanted to receive the MOST possible dog biscuits? because 4 frisbees and 3balls would mean only 29 biscuits.
• she does not want to receive the most dog biscuits, she wants to receive as most 30 but any below that is also okay. as the point you said is not on the line but below it she would not get the maximum amount as with any other point below the line. again as the equation to this is 5F + 3B ≤ 30. 29 works
• I do not think Diana fulfilled her plan. At (4,2) Diana still had NOT received MOST biscuits, therefore not fulfilling her plan.
• Diana does fulfill her plan because she wants to get AT MOST 30 biscuits, not more than that. She is okay with getting some biscuits less than 30! The point (4,2) is in the shaded area which means she is fulfilling her plan as she has less than 30 biscuits.
5F + 3B ≤ 30 => F= 4 & B= 2 => 5(4) +3(2) ≤ 30 => 20+6 ≤ 30 => 26 ≤ 30!
So, yes she does fulfill her plan!
• so would i write "at most" as less than, greater than, less than or equal to or greater than and equal to?
(1 vote)
• Less than and equal to
• Bruh. Where did the 30 come from?
(1 vote)
• She gets 3 biscuits for every ball, so after fetching 10 balls and no frisbees, she'd have 30 biscuits
• ERROR in my question of 5 minutes.
I made an elementary mistake as the equation is NOT :
B= -5/3F +D but
B= -5/3F +D/3
Correction between angle brackets (<>) has been inserted below in my original question :

"From the problem "wording" I can derive the Diophantine equation D=5F+3B or B=-5/3 F + D</3> which corresponds to a bunch of parrallel lines with negative slope -5/3 and y-intercept= D</3> and D still unknown. So how can I from these incomplete data derive the graph? From which data did Sal derive that the y-intercept equals 10 <so D=30> rather than any other value?"
(1 vote)
• The graph was given as part of the problem. So, it did not need to be derived. Without the graph, there isn't sufficient info to determine the graph for the line.
(1 vote)
• I'm trying my best to understand but the graph is making me confused, is there another that it can be explained.
• Is the reason we don't say the maximum number of biscuits the dog can get is 5(6)+3(10)=60 is because the graph connects between the points (0,10) and (6,0)? if it included the point (6,10) we could've said the dog can get the max no. of biscuits for both the balls and Frisbee and that would be 60, right?
• Even though this seems like a real life word problem, it really isn't because dogs can't do the math. What actual real life word problems would work for inequalities?
• The ones about going to fair and you have 20 dollars to spend, it costs 5 dollars to get in, some rides are 25 cents and some are 50 cents. If you want to ride at least 10 rides, what are some possible combinations of 25 and 50 cent rides?
Anytime you have a limited amount of money to spend, you can figure out what you might want to buy.
This can get bigger scale if you are talking about a company and the amount of inventory you might want keep on hand to maximize profits.
With launching rockets, you have to balance how much fuel you will need with the weight to launch the rocket.
• How we should know that x-axis is the number of frisbees and not the number of balls or vice- versa how to know that. How he assumed that. *Can please anyone help?*
• First - the graph was given along with the text description of the problem. You need to read word problems very carefully. It pays to read them more than once to make sure you understand what info you are being given.

In the 2nd paragraph, it tells you the F=# of frisbees and B=# of balls. So, then look at the graph. The x-axis is labeled with "F". So, the graph is telling you that it is number of frisbees if you know that F=# of frisbees. Similarly, the y-axis is labeled "B", so it tells you that is it number of balls.

Hope this helps.
• I wondered how she would fulfill her plan of reaching D, when we found out that D is the maximum number of dog biscuits equal to 30. Original equation: 5F + 3B = D,
F=4 and B=2.
5(4) + 3(2) = D
20 + 6= D
26=D
However we already know that D is actually equal to 30 using the graph so
26=30 is not correct, and so does not satisfy the inequality. And so the answer would be no because her plan of getting D biscuits was not achieved.
Or am I not understanding this?
• It only means that anything`<=30` is OK. Even 3 biscuits are OK.