Application Practice
Answer the following questions. If appropriate, use Equation Editor to show your work. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
Each part is worth 2 points.
1. This coming summer, we are meeting up with some other family members at Family Fiesta Amusement Park. The ticket price for children is $17 and for adults the ticket price is $31. The total price for all 20 of us to enter the park is $438.
a. Write an equation, using A for adults and C for children, that illustrates the number of tickets bought.
b. Write an equation, using A for adults and C for children, that illustrates how much money was spent.
c. Use the Elimination Method or Addition Method to determine how many adult tickets and how many childrens tickets were purchased. Show your work, or no credit will be awarded. No credit will be awarded for guessing to find the answer.
d. Would a value of -10 make sense for A? Explain why or why not.
2. While at the amusement park, the Tunmire family bought 8 hot dogs and 5 soft drinks for lunch, which cost $15.05. Then the Lee family bought 13 hot dogs and 9 soft drinks for $25.20.
a. Write an equation, using H for the cost of a hot dog and S for the cost of a soft drink, that illustrates the cost of what the Tunmire family bought.
b. Write an equation, using H for the cost of a hot dog and S for the cost of a soft drink, that illustrates the cost of what the Lee family bought.
c. Using the Elimination Method or the Addition Method, determine the cost of one hot dog and one soft drink. Show your work, or no credit will be awarded. No credit will be awarded for guessing to find the answer.
3. (a) Make up a system of two linear equations containing two variables that has no solution.
(b) Explain what both equations have in common.
4. Based on the graph below, identify the point of intersection.
To answer the questions, we will break them down one by one:
**Question 1:**
a. The equation that illustrates the number of tickets bought can be written as:
A + C = 20
b. The equation that illustrates how much money was spent can be written as:
31A + 17C = 438
c. To determine how many adult tickets and how many children's tickets were purchased, we can solve the system of equations using the elimination method or the addition method.
Elimination Method:
Multiply the first equation by 17 to make the coefficient of C the same as in the second equation:
17(A + C) = 17(20) -> 17A + 17C = 340
We can subtract this new equation from the second equation to eliminate the C term:
(31A + 17C) - (17A + 17C) = 438 - 340
14A = 98
Divide both sides by 14:
A = 7
Now substitute the value of A back into the first equation to find C:
7 + C = 20
C = 20 - 7
C = 13
So, 7 adult tickets and 13 children's tickets were purchased.
d. A value of -10 for A does not make sense because the number of tickets cannot be negative and it does not fit the context of the problem. In this case, A represents the number of adult tickets, so it should be a positive integer.
**Question 2:**
a. The equation that illustrates the cost of what the Tunmire family bought can be written as:
8H + 5S = 15.05
b. The equation that illustrates the cost of what the Lee family bought can be written as:
13H + 9S = 25.20
c. To find the cost of one hot dog and one soft drink, we can solve the system of equations using the elimination method or the addition method.
Elimination Method:
Multiply the first equation by 13 and the second equation by 8 to make the coefficients of H in both equations the same:
104H + 65S = 195.65
104H + 72S = 201.60
We can subtract the first equation from the second equation to eliminate the H term:
(104H + 72S) - (104H + 65S) = 201.60 - 195.65
7S = 5.95
Divide both sides by 7:
S = 0.85
Now substitute the value of S back into the first equation to find H:
8H + 5(0.85) = 15.05
8H + 4.25 = 15.05
8H = 10.8
H = 1.35
So, the cost of one hot dog is $1.35 and the cost of one soft drink is $0.85.
**Question 3:**
a. A system of two linear equations that has no solution could be:
2x + 3y = 5
4x + 6y = 10
b. Both equations have the same slope (2/3) and the same y-intercept (5/3), meaning their graphs are parallel lines. Since they never intersect, there is no solution.
**Question 4:**
Based on the graph, it is not provided. Please provide the specific graph or additional information for me to identify the point of intersection.
I hope this helps! Let me know if you have any further questions.