How do you solve this?

[Anonymous No.11595865]

A woman in charge of shipping packages for Amazon can place 8 large boxes or 10 small boxes into a Prime carton for shipping. In one shipment, she sent a grand total of 96 boxes. If there are more large boxes than small boxes, what is the smallest number of Amazon Prime cartons she could have shipped?

[Anonymous No.11595901]

>>11595865
system of linear equations

[Anonymous No.11595912]

>>11595901
actually a system of linear inequalities

[Anonymous No.11596070]

>>11595901
>>11595912
nevermind this is some topology bullshit isn't it

[Anonymous No.11596082]

>>11596070
To be honest it's a question a place I'm applying to wants you to fill the answer into a box before sending the application.

[Anonymous No.11596100]

>>11595865
Just thinking about it is probably the easiest way.

Since small boxes come in a carton of 10, you know that your sum total of large boxes has to end in '6' to add up to 96.

From 0 to 96, there's only two multiples of 8 that end in 6. One is 16 and the other is 56.

16 isn't greater than 48 (half of 96), so it fails the condition "more large boxes than small boxes". 56 large boxes means there's 40 small boxes. Therefore, the number of cartons is 56/8 + 40/10 = 7 + 4 = 11.

[Anonymous No.11596109]

>>11596082
well so far I've gotten that you can express the problem as an ellipse [math]\frac{1}{8}a^2+\frac{1}{10}b^2=96[/math] where [math]a>b>0[/math]
so the answer is going to involve one of the combinations of this curve

[Anonymous No.11596123]

>>11596100
Yes, that seems to be the correct solution. Thank you very much whoever you are. Do you know of any websites that allows you to practice problems like this one?