writing an inequality

Question

I need to sell 300 cupcakes at 3.00 each in order to make back the money I spent on ingredients. Write an inequlaity to determine homw many cupcakes i need to sell in order to make 100.00 profit.

Answer 1

Well, that's interesting wording. Making $100 profit is just that, but making at least $100 profit is an inequality.

So, if you sell 2 cupcakes, you've made $3(2), right? We'll call the number of cupcakes you actually sell c. You'll then be making $30c, whatever number we sell that takes the place of c.

Profit is what you make after subtracting cost. Since we need to make $100 or more, our equation seems like it should be...

3c - 300 ≥ 100

There's just one problem. 3c gives us a dollar amount, and 300 is the number of cupcakes we need to sell and not a dollar amount. If we sell 300 cupcakes, we make $3(300), our break even point.

3(c - 300) ≥ 100

Distributing, we end up with...

3c - 900 ≥ 100

In other words, the we have to sell c cookies at $3 each and subtract the sales of 300 cupcakes ($900) to get our profit, which we want to be $100 or more.

Hope this helps!

Answer 2

300*3=900cost

100/3=34cupcakes

=334 cupcakes needed to make $100 profit.