Answer: 15x - 1500 > 0, 101 batches
Explanation:
To begin, lets start by modeling this with a linear equation, (for sake of simplicity).
we can model this in the form y = mx + b, where y is 0, (meaning she isn't making profit OR losing money either).
Next, lets set up the parameters:
0 = mx + b. We can safely say that b, our constant, is -1500, because this is the money she "loses" every month.
Now we have 0 = mx -1500. We know she sells each batch for $20, so we also know that she makes 20x dollars for x batches. Our m = 20.
Now we have 0 = 20x - 1500. However, this equation is not completely correct, as we arent subtracting the cost for making each batch of cupcakes. The problem says that it costs her $5 to make each batch. So it will cost her 5x dollars for making x batches. If we subtract this from how much she sells each batch for, we get the profit she makes from selling each batch. So she makes a profit of (20x - 5x) = 15x dollars for x batches of cupcakes.
Out completed equation is 15x - 1500 = 0.
Solving this equation for x will give us how many batches she needs to sell to break even. To model this as an inequality for profit we simply replace the "=" sign with a ">" sign.
So our completed inequality is 15x - 1500 > 0
Solving this for x:
15x - 1500 > 0
15x > 1500
x > 100
Amanda needs to make more than 100 batches per month to make a profit. The greatest number of whole number batches over 100 is 101; so she needs to sell atleast 101 batches to make a profit every month.