Question

a high school drama club is fundraising for an upcoming event. they decide to sell custom designed t - shirts and hoodies. each t - shirt cost $15 and each hoodie cost $25. in the first week, they sold a total of 50 items and made $900. which graph represents the t - shirts and hoodies sold? t+h = 50 15t + 25h = 900 which graph represents this situation?

Explanation:

Step1: Rewrite equations in slope - intercept form

The equation $t + h=50$ can be rewritten as $t=-h + 50$. Its $y$-intercept is 50 and slope is - 1.
The equation $15t+25h = 900$ can be rewritten as $t=\frac{900 - 25h}{15}=60-\frac{5}{3}h$.

Step2: Find intercepts

For $t=-h + 50$, when $t = 0$, $h = 50$; when $h = 0$, $t = 50$.
For $t=60-\frac{5}{3}h$, when $t = 0$, $0=60-\frac{5}{3}h$, then $\frac{5}{3}h=60$, $h = 36$; when $h = 0$, $t = 60$.

Step3: Analyze graphs

We are looking for a graph where one line has a $y$-intercept of 50 and slope - 1 and the other has a $y$-intercept of 60 and a negative slope of $-\frac{5}{3}$.
The first equation $t + h=50$ represents a line with points like $(0,50)$ and $(50,0)$. The second equation $15t+25h=900$ represents a line with points like $(0,36)$ and $(60,0)$.

The graph that has a line passing through $(0,50)$ and $(50,0)$ and another line passing through $(0,36)$ and $(60,0)$ is the correct one.

Answer:

The graph where one line has $t$-intercept 50, $h$-intercept 50 and the other line has $t$-intercept 60, $h$-intercept 36. (Since no specific graph is labeled as correct among the options in the text, this is a description - if there were labeled graphs, we'd identify the one matching the above - described intercepts).