you have $200 to buy stationary. A box of envelopes cost $8. a box of paper cost $10. which inequality describes how many of each box can you buy ?

Answer 1

Hi Hennise! To start this one, let us review what we know. We know that at maximum we have $200 we can spend. Since we don’t have any more, whatever we do end up spending, it has to be exactly $200 or less. Otherwise, we wouldn’t be able to afford it. The next part we need to look at is that there are two items we are considering buying: envelopes and paper. Since we left the amount we could buy of each open, the only thing that is stopping us from buying hundreds of each is that we only have $200 at max.

The tricky part about inequalities is that they usually leave the amount of items you can buy pretty open which means if I wanted, I could take the $200 and at $10 per pack of paper, I could buy 20 packs and no envelopes. On the other hand, I could buy 25 packs of envelopes at $8 per box and no paper. To relate this, we know that if we buy any amount in between those two extremes, they will have a unique combination of paper and envelop that ultimately costs under $200. Since we can have a lot of different possible packs of paper or envelop, we can substitute in any numbers we buy with generic variables of your choice (let’s use X and Y for simplicity, but if you wanted, you could use any other letters). We know that paper is $10, and to buy an untold number more, we can represent that with X ($10 x X) The same goes with envelopes. We can buy an untold amount more, so it can be represented as $8 x Y. Overall, we know any combination has to be less than or equal to $200, so $10X + 8Y less than or equal to $200.

I hope this helps!