For each t-shirt sold, which I'll call t, 8th grade makes $15.
For each hat sold, which I'll call h, 8th grades makes $5.
They want to raise $900
A: The equation to represent this situation is 15t+5h=900 because if 8th grade adds up all the profits from both hats and t-shirts, the goal is to make $900, so the total profit from shirts and hats should equal 900 dollars.
B: I'm just going to choose random numbers. Let's say nobody wanted to buy a hat from the 8th graders (h=0). You'd end up with
15t+5(0)=900
15t=900
t=60 - If they sold 0 hats they would have sold 60 shirts to raise $900
Now let's say it was the other way around - nobody wanted to buy t-shirts
15(0)=5h=900
5h=900
h=180 - If they sold 0 t-shirts they'd have to sell 180 hats to raise $900
Finally let's say they sold 30 t-shirts
15(30)+5h=900
450+5h=900
5h=450
h=90 - They'd have to sell 30 t-shirts and 90 hats to raise $900
