Question

b. you have $75 to spend. how many competitions can you attend?
you can attend \boxed{} competitions.

Explanation:

Step1: Define linear equation

First, identify the two points on the line: (0, 50) (y-intercept) and (10, 0). The slope $m = \frac{0-50}{10-0} = -5$. The equation of the line is $y = -5x + 50$, where $y$ is total money left, $x$ is number of competitions.

Step2: Set up cost equation

We have $75 total, so total money spent on competitions is $75 - y$. But since when $y=0$, we spent $50 for 10 competitions, each competition costs $5. So total cost for $x$ competitions is $5x$. We set $5x \leq 75$.

Step3: Solve for x

$\frac{5x}{5} \leq \frac{75}{5}$
$x \leq 15$
But check the original line's context: the line shows up to 10 competitions uses $50, but the cost per competition is constant at $5. So with $75, we calculate the maximum number.

Answer:

15