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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 worry about Diana's health. 5 biscuits per frisbee is way too much! She's probably eating over a hundred biscuits every time they go to the park.
• If you watched the whole video, it appears that Diana maxes out at 30 biscuits.
• 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
(1 vote)
• I'm trying my best to understand but the graph is making me confused, is there another that it can be explained.
(1 vote)
• 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?
(1 vote)
• It only means that anything`<=30` is OK. Even 3 biscuits are OK.
(1 vote)
• 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?
(1 vote)
• 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!
• I don't understand what the last question in this example was trying to illustrate?
• 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.