Question 1 A)For a large group of students, the Boston Ballet charges a flat rate of $50.00, plus $15.00 per ticket. How much would a school need to take a class of 25 students to see The Nutcracker? Use an equation with two variables to solve this problem.(1 point) Responses $425.00 $425.00 $50.00 $50.00 $1,265.00 $1,265.00 $375.00 $375.00 Question 2 A)The school soccer team is selling chips to fundraise for new jerseys. If they charge $2.50 per bag of chips, how many bags would they need to sell in order to raise $1,000.00?(1 point) Responses $400.00 $400.00 40 bags 40 bags 400 bags 400 bags 500 bags 500 bags Question 3 A)Which of the following examples represents a discrete data constraint with viable solutions?(1 point) Responses distance between points distance between points number of tests passed number of tests passed average weight of all the newborns in a hospital ward average weight of all the newborns in a hospital ward average score on a test average score on a test Question 4 A)Which of the following options could use both intercepts to produce viable solutions? (1 point) Responses (age, weight) (age, weight) (number of nominations, number of awards) (number of nominations, number of awards) (temperature, number of car rentals) (temperature, number of car rentals) (years of experience, starting salary) (years of experience, starting salary) Question 5 A)Cindy won $50.00 for getting first place in the Science Fair. She spent her winnings on robotics kits and chemistry sets. Each robotics kit (y) costs $10.00, while each chemistry set costs $8.00 (x). Which of the following is a viable solution to the number of robotics kits and chemistry sets Cindy can purchase, assuming she spends her entire winnings?(1 point) Responses (−5,9) left parenthesis negative 5 comma 9 right parenthesis (5,1) left parenthesis 5 comma 1 right parenthesis (3,2.6) left parenthesis 3 comma 2.6 right parenthesis (0,5) left parenthesis 0 comma 5 right parenthesis

Answer 1

Let's break down each question and find the correct answers.

Question 1

Problem: The Boston Ballet charges a flat rate of $50.00 plus $15.00 per ticket. The school wants to take a class of 25 students to see The Nutcracker.

Equation: Let \( x \) be the number of students (25) and \( y \) be the total cost. \[ y = 50 + 15x \]

Calculating the total cost: \[ y = 50 + 15(25) \] \[ y = 50 + 375 \] \[ y = 425 \]

Response: $425.00

Question 2

Problem: The school soccer team is raising funds by selling chips at $2.50 per bag and wants to raise $1,000.

Equation: Let \( b \) be the number of bags sold. \[ 2.50b = 1000 \]

Calculating the number of bags needed: \[ b = \frac{1000}{2.50} \] \[ b = 400 \]

Response: 400 bags

Question 3

Problem: Identify an example that represents a discrete data constraint with viable solutions.

Discrete data is countable, like the number of something (e.g., tests passed).

Response: number of tests passed

Question 4

Problem: Identify which options could use both intercepts to produce viable solutions.

Options that can produce both x and y intercepts generally involve two quantitative variables.

Response: (number of nominations, number of awards)

Question 5

Problem: Cindy wants to spend her $50.00 on robotics kits ($10 each) and chemistry sets ($8 each).

Let \( x \) be the number of chemistry sets, and \( y \) be the number of robotics kits.

Equation: \[ 8x + 10y = 50 \]

Testing each option:

1. (−5, 9): \[ 8(-5) + 10(9) = -40 + 90 = 50 \] (Viable solution, but negative not possible)

2. (5, 1): \[ 8(5) + 10(1) = 40 + 10 = 50 \] (Viable solution)

3. (3, 2.6): \[ 8(3) + 10(2.6) = 24 + 26 = 50 \] (Invalid as y should be an integer)

4. (0, 5): \[ 8(0) + 10(5) = 0 + 50 = 50 \] (Viable solution)

Response: (5, 1)

Summary of Responses:

1. $425.00
2. 400 bags
3. number of tests passed
4. (number of nominations, number of awards)
5. (5, 1)