If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# 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.

## Want to join the conversation?

• 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.
• 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?
• Less than and equal to
• Bruh. Where did the 30 come from?
• She gets 3 biscuits for every ball, so after fetching 10 balls and no frisbees, she'd have 30 biscuits
• The problem is silly. The dog's 'plan' seems to be to minimize food intake and maximize exercise (fetching + chasing it's tail). Like a person taking up a diet and exercise regime.

Since when do dogs do that!?
(1 vote)
• Maybe the problem is silly because it was designed for kids.
(1 vote)
• I'm trying my best to understand but the graph is making me confused, is there another that it can be explained.
• She only wants to receive 30 at most
• 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?
• 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.