Question

Katie wrote a book and wants to publish it herself. She created the equations below to represent the cost to publish her book and the income she makes selling the book. How many books, x, will she need to sell in order for her income to be equal to the cost to publish her book?
Cost: y = 5x + 480
Income: y = 11x

Answer 1

To find out how many books, \( x \), Katie needs to sell for her income to equal her costs, we need to set the equations for cost and income equal to each other:

1. Cost: \( y = 5x + 480 \)
2. Income: \( y = 11x \)

Setting these two equations equal gives us:

\[
5x + 480 = 11x
\]

Now, we can solve for \( x \):

1. Subtract \( 5x \) from both sides:

\[
480 = 11x - 5x
\]

\[
480 = 6x
\]

2. Divide both sides by 6:

\[
x = \frac{480}{6}
\]

\[
x = 80
\]

Therefore, Katie needs to sell **80 books** for her income to equal her cost.