Project 2~Applications with Linear Systems of Equations 5-Steps for Problem Solving
This project is worth 16 points. For each of the following exercises 1-4: Solve the applications using “5 Steps for Problem Solving” as described in the notes notes within Chapter 4 from the menu at the left in our Blackboard course and shown below. Number and show all 5 steps on paper for each word problem.
Example: Admission to the Indianapolis Children’s Museum costs $5.50 more for an adult than for a child (Source: Indianapolis Children’s Museum). Admission to the museum for Barbara and Jeff Johnson and their five children costs $39. Find the cost of each adult’s admission and each child’s admission.
1.Let x = adult admission price
and y = child admission price
2.Using a chart to organize the given information:
Number of tickets
? Price per ticket (in $)
= Expenses (in $)
Adults
2
x
2x
Children
5
y
5y
Total
7
39
Also given that ticket price for adults is $5.50 more than for children: x = y + 5.50
3.x = y + 5.50(Admission costs $5.50 more for adults than for children)
2x + 5y = 39 (Total expenses for the family is the sum of the expenses from each type of ticket)
4.Solving the system by substitution:2(y + 5.50) + 5y = 39
2y + 11 + 5y = 39
7y = 28
y = 4
Substituting y = 4 into the first equation from the system: x = 4 + 5.50 = 9.50.
5.Adult admission is $9.50 and a child’s admission is $4 to the Indianapolis Children’s Museum.
FIVE STEPS FOR PROBLEM SOLVING WITH SYSTEMS OF EQUATIONS
1.Determine what you are to find. Assign a variable for each unknown and writedown what it represents: let x = ______, y = _____, etc.
2.Organize and label all given or known information. If appropriate, draw a figureor a diagram and label it using the variables for Step 1. Use a chart to organize thegiven information, including formula, variables, totals, etc.
3.Write a system of equations. Write as many equations as there are unknowns.
4.Solve the system.
5.Answer the question(s). Be sure you have answered all questions posed using acomplete sentence with the appropriate units.
1.Annual Concert. A total of 150 tickets were sold for the annual concert to students and nonstudents. Studenttickets were $5 and nonstudent tickets were $8. If the total revenue for the concert was $930, then how many tickets of each type were sold?
2.Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. Ifpart of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?
3.Nickels and dimes. Winborne has 35 coins consisting of dimes and nickels. If the value of his coins is $3.30, thenhow many of each type does he have?
4.Three-day drive. In three days, Carter drove 2196 miles in 36 hours behind the wheel. The first day he averaged 64mph, the second day 62 mph, and the third day 58 mph. If he drove 4 more hours on the third day than on the first day, then how many hours did he drive each day?