Questions: Two parents take their N children to movies. Adult tickets are 9 each and child tickets are 7. They buy a 3 box of popcorn for each child and pay 6 for parking. Find an expression for the cost of the excursion. C(N)= dollars Is the expression linear in N ? Choose one

Two parents take their N children to movies. Adult tickets are 9 each and child tickets are 7. They buy a 3 box of popcorn for each child and pay 6 for parking. Find an expression for the cost of the excursion. C(N)= dollars Is the expression linear in N ? Choose one
Transcript text: Two parents take their $N$ children to movies. Adult tickets are $\$ 9$ each and child tickets are $\$ 7$. They buy a $\$ 3$ box of popcorn for each child and pay $\$ 6$ for parking. Find an expression for the cost of the excursion. \[ C(N)= \] dollars Is the expression linear in $N$ ? Choose one
failed

Solution

failed
failed

Solution Steps

To find the expression for the cost of the excursion, we need to consider the cost of adult tickets, child tickets, popcorn, and parking. The total cost will be the sum of these components. Since there are 2 adults, the cost for adult tickets is fixed. The cost for child tickets and popcorn depends on the number of children, \( N \). The parking cost is also fixed. We will then determine if the expression is linear in \( N \).

Step 1: Calculate the Cost of Adult Tickets

The cost for adult tickets is fixed since there are 2 adults. Each adult ticket costs \$9. Therefore, the total cost for adult tickets is: \[ 2 \times 9 = 18 \]

Step 2: Calculate the Cost of Child Tickets

The cost for child tickets depends on the number of children, \( N \). Each child ticket costs \$7. Therefore, the total cost for child tickets is: \[ N \times 7 = 7N \]

Step 3: Calculate the Cost of Popcorn

Each child gets a box of popcorn costing \$3. Therefore, the total cost for popcorn is: \[ N \times 3 = 3N \]

Step 4: Calculate the Cost of Parking

The parking cost is fixed at \$6.

Step 5: Formulate the Total Cost Expression

The total cost of the excursion, \( C(N) \), is the sum of the costs calculated in the previous steps: \[ C(N) = 18 + 7N + 3N + 6 \] Simplifying the expression, we get: \[ C(N) = 24 + 10N \]

Step 6: Determine if the Expression is Linear

The expression \( C(N) = 24 + 10N \) is linear in \( N \) because it is in the form \( a + bN \), where \( a \) and \( b \) are constants.

Final Answer

The expression for the cost of the excursion is: \[ \boxed{C(N) = 24 + 10N} \] The expression is linear in \( N \).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.78, given that a person has tuberculosis. The probability is 0.07 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.03. What is the probability that a person chosen at random will fall in the following categories. (a) have tuberculosis and have a positive test (b) not have tuberculosis (c) not have tuberculosis and have a positive test
failedAnswered
x1 y1 1 -5 2 -5 3 9 4 49 5 125 6 255 7 445 y1 sim a x^3 + b x1^2 + c x1+d
failedAnswered
Solve the equation 16x^3+16x^2-x-1=0 given that -1/4 is a zero of f(x)=16x^3+16x^2-x-1
failedAnswered
Round answer to proper number of significant figures. 2.74-0.00072=
failedAnswered
With a child that weighs 7 kg, which piece of equipment should be used to obtain a blood pressure? A child blood pressure cuff. An infant blood pressure cuff. A newborn blood pressure cuff. A BP cuff that is 1 / 3 the width of the upper arm.