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Writing systems of inequalities word problem

Sal models a word problem about baking cupcakes and muffins by creating a system of linear inequalities.

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• I have no idea what i am doing!
• I know that feeling. Try to understand what he is saying intuitively. Then it will come out faster than the alphabet.
(1 vote)
• If you graph them, do you get the "feasible region" in other problems?
• If there is/are solutions that satisfy both conditions, then yes, when you plot it, it will show the feasible regions. If there is no true answer then no, there will not be a feasible region.
• Does 'At most' always refer to 'Less than or equal to'
• not always but yes .
• Can you write an inequality that represents the amount of cupcakes made or muffins made? Or is the information insufficient/impossible to solve for?
• I don't think so.
We have in the first sentence an inequality based on sugar and then in the second inequality we have all setup based on flour.

Even if we have the same variable, C and M their constants and meaning aren't the same.
• Just want to confirm something, so in inequality the solution is not just one, but many as long as in shaded area right?
• all comments are so far back when someone replies to this I'll be I don't know really old
• The last comment on this subject was 5 months ago, sort the answers by most recent, not top voted. You are not even a day older than when you wrote your comment.
• Can this system of inequalities be solved?
• it is solvable, but the big numbers might make it harder to solve unless you use a graphing calculator such as DESMOS which is a free on-line calculator. This will show a double shaded region with possible solutions, but you can only use the whole number solutions, it looks like somewhere between 40 to 50 possible solutions.
(1 vote)
• How would you solve this system of inequalities?

Would elimination/substitution work?
• Yeah you could use both. They're both compatible
(1 vote)
• to think I forgot what at most and at least even meant
(1 vote)
• "At most" means that it can be less than or equal to. "At least" means that it can be greater than or equal to.