Question

1. the 24 students in ms. cleary’s homeroom are surveyed. they are asked which of several prices they would pay for a ticket to the school fashion show. the table shows the results.

ticket-price survey

ticket price	$1.00	$1.50	$2.00	$2.50	$3.00	$3.50	$4.00	$4.50

image of tickets: middletown high school presents: the spring fashion show featuring mathematical models, friday, may 23, at 7:00 pm, middletown high school auditorium

a. there are 480 students in the school. use the data from ms. cleary’s class to predict ticket sales for the entire school for each price.

b. use your results from part (a). for each price, find the school’s projected income from ticket sales.

c. which price should the school charge if it wants to earn the maximum possible income?

Explanation:

Part (a)

Step1: Find the ratio of school students to homeroom students.

The number of students in the school is 480, and in Ms. Cleary's homeroom is 24. The ratio is $\frac{480}{24} = 20$.

Step2: Multiply each probable sales in homeroom by the ratio to get school sales.

• For \$1.00: $20\times20 = 400$
• For \$1.50: $20\times20 = 400$
• For \$2.00: $20\times18 = 360$
• For \$2.50: $20\times15 = 300$
• For \$3.00: $20\times12 = 240$
• For \$3.50: $20\times10 = 200$
• For \$4.00: $20\times8 = 160$
• For \$4.50: $20\times7 = 140$

Part (b)

Step1: Recall the formula for income: Income = Price × Sales.

Step2: Calculate income for each price using part (a) results.

• For \$1.00: $1.00\times400 = 400$
• For \$1.50: $1.50\times400 = 600$
• For \$2.00: $2.00\times360 = 720$
• For \$2.50: $2.50\times300 = 750$
• For \$3.00: $3.00\times240 = 720$
• For \$3.50: $3.50\times200 = 700$
• For \$4.00: $4.00\times160 = 640$
• For \$4.50: $4.50\times140 = 630$

Part (c)

Step1: Compare the incomes calculated in part (b).

The incomes are: \$400, \$600, \$720, \$750, \$720, \$700, \$640, \$630.

Step2: Identify the maximum income and its corresponding price.

The maximum income is \$750, which corresponds to a ticket price of \$2.50.

Answer:

s:
a.

Ticket Price	\$1.00	\$1.50	\$2.00	\$2.50	\$3.00	\$3.50	\$4.00	\$4.50

b.

Ticket Price	\$1.00	\$1.50	\$2.00	\$2.50	\$3.00	\$3.50	\$4.00	\$4.50

c. The school should charge \$2.50.