Superlesson
Project 4-2
Algebra
Chapter 4
Solving Linear Equations and Inequalities
San Francisco Zoo is one of the most famous zoos in the world. You can use the Internet to find out how much it costs to visit the zoo.
Part A, Algebra Tiles
1. Suppose the curator of San Francisco Zoo wanted to know how much income the zoo earns from admission fees paid by adult residents of San Francisco. You can find the information at the San Francisco Zoo Web site.
a. Complete the table below showing the income the zoo earns from admission fees paid by adults (ages 16-64).
A
Number of Adults
1
2
3
5
10
I
Income
b. Express this information as an equation with I = income and A = number of adults.
c. Suppose that the income from admission fees paid by adult residents of San Francisco was $21,000 for the month of October. Use your equation from b to find the number of paying adult residents who visited the zoo.
d. How could you use algebra tiles to model your equation? Explain your answer.
Part B, Connecting Algebra Tiles to Symbols
2. The Smiths and their two children (ages 6 and 9) are planning a trip to the San Francisco Zoo. They will need to pay admission fees for two adults and two children. They also want to purchase tickets for all of them to ride the Carousel and the Safari Train one time.
a. Write an equation expressing the least expensive total cost for the Smith family to visit the zoo and take their rides. Let T = total cost, A = the number of adults, and C = the number of children. Calculate the total cost for the Smith family's zoo visit.
b. One adult and several children each bought the Safari Saver package for admission to the zoo. The total cost for this group was $26.00. How many children were in the group?
HINT: To model this situation using algebra tiles, use yellow strips to represent the number of children and yellow squares to represent dollars.
Part C, Properties of Equality
3. The students at the Fairbanks School are planning to visit the San Francisco Zoo. The school is 320 miles from the zoo.
a. Using the formula d = r · t, about how long should the trip take if the bus driver travels at an average speed of 55 miles per hour? 65 miles per hour? 50 miles per hour?
b. Based on your information from a, would it be reasonable for the Fairbanks School students to plan a one-day trip for their zoo visit? Explain your thinking.
Part D, Simplifying to Solve Equations
4. Suppose that the San Francisco Zoo needs an income of $370,000 in every two-day period to cover their operating expenses.
a. If 15,000 adults attend the zoo each Monday and 22,000 adults attend the zoo each Tuesday, how much must the zoo charge to cover their operating expenses? Write an equation to represent this situation and then solve your equation.
b. If only children were to attend the zoo on Wednesdays and Thursdays and the admission for each child is $6.25, how many children need to visit the zoo in order to meet the zoo's operating expenses? Write and solve an equation to represent this situation.
Part E, Making Connections
5. An annual zoo membership costs $55.00 per family. The Smith family (from Part B) is planning to purchase a one-year membership.
a. At what point does the cost of an annual membership equal the cost of single-day visits?
b. In what circumstances will it be more economical for the Smith family to buy an annual zoo membership?