Grade 6 Algebra - 2 Unknowns in the problem

[Hannah1291]

Hello:

I am trying to help my daughter with her grade 6 math and I'm stuck. I would really appreciate any help you can give.

Question: A company makes 150 bags of rice per day. Some of the bags weigh 45 KG and other bags weigh 36 KG. The total daily production is 5958 KG. How many bags of each type are there? Give at least 2 possibilities.

I figured out one possibility (62 bags of 45 KG and 88 bags of 36 KG) but I am stuck on a second possible answer. I don't think there is one. Am I incorrect?

Thanks!

 

[MarkFL]

Suppose \(X\) is the number of 36 kg bags and \(Y\) is the number of 45 kg bags, and so we get from the problem statement the following linear system:

[MATH]X+Y=150[/MATH]
[MATH]36X+45Y=5958[/MATH]
This system has one solution:

[MATH](X,Y)=(88,62)[/MATH]
And this is what you found. There is no other possibility.

 

[Hannah1291]

Thank you so much!