Question

The school council is raising money for a field trip to the state capital. To raise money, members are renting a cotton candy machine and selling cotton candy at lunch. They need to raise at least $180 for the trip, and figure that they can sell cotton candy to 85 students at $3 each.
A. Write an inequality that can be used to determine how much they can afford to pay for the cotton candy machine.


B. What is the price they can afford to pay for the cotton candy machine?




2. A hot air balloon, including the basket underneath to hold its passengers, weighs 140 pounds. The apparent weight of the balloon is given by the equation below.

apparent weight = weight – lift
If the apparent weight is 0 or less, the balloon will float.

A. The balloon has a lift of 400 pounds. Write an inequality that could be used to determine how heavy the passengers of the balloon can be.


B. Use your inequality to calculate how much the passengers can weigh.


C. There is a second balloon, which has a different weight but the same amount of lift. With no passengers, the apparent weight of the balloon is -130 pounds. What is the weight of the balloon?

Answer 1

1A. $3*85 - C >= $180 1B. $75 >= C 2A. (P + 140) - 400 <= 0 2B. P <= 260 2C. W = 270 1A. The money raised by the cotton candy machine will be the money earned minus the cost. So $3*85 - C >= $180 1B. Solve for C $3*85 - C >= $180 $255 - C >= $180 $255 >= $180 + C $75 >= C So the cost of the cotton candy machine (including supplies) has to be less than or equal to $75. 2A. Let's use P as passenger weight. (P + 140) - 400 <= 0 2B. Solve for P (P + 140) - 400 <= 0 P + 140 - 400 <= 0 P + 140 <= 400 P <= 260 So the passengers can weigh at most 260 lbs. 2C. Since the lift is 400 and the apparent weight is -130, the equation is W - 400 = -130 Solving for W gives W - 400 = -130 W = 270 So the other balloon weights 270 pounds.