4.1.2
Systems of Equations (continued)
Name: _____________________________
I Can _____________________________________________________________________________.
Example 1: The equations 5x + 2y = 48 and 3x + 2y = 32 represent the money collected from school concert
ticket sales during two class periods. There were more adult tickets sold than student tickets.
What was the price of an adult ticket?
Define the variables. Let x =
y=
What does each equation represent?
Solve the system and answer the question.
Example 2: Bill and Steve decide to spend the afternoon at an amusement park enjoying their favorite
activities, the water slide and the gigantic Ferris wheel. Their tickets are stamped each time they
slide or ride. At the end of the afternoon they have the following tickets:
Bill’s Ticket
Steve’s Ticket
Fun Time Amusements
Fun Time Amusements
Water Slide:
Water Slide:
Ferris Wheel:
Ferris Wheel:
Total: $17.70
Total: $15.55
How much does to cost to ride the Water Slide?
_________________________
`How much does it cost to ride the Ferris Wheel? _________________________
Define the variables: Let x =
y=
Write an equation showing that Bill spent a total of $17.70 on rides.
Write an equation showing that Steve spent a total of 15.55 on rides.
Solve the system of equations and answer the questions.
Example 3: Michelle is making goodie bags for Christmas filled with chocolates and candy. Chocolates cost
$2.50 per lb. and candy costs $3.00 per lb. Michelle bought 15lbs. for $40. How many lbs. of
chocolate and how many lbs. of candy did Michelle buy?
Define the variables: Let x =
y=
Write an equation showing that Michelle spent a total of $40 on chocolates and candy.
Write an equation showing that Michelle bought a total of 15 lbs. of chocolates and candy.
Solve the system of equations and answer the questions.
Example 4. The Lopez family had a rectangular garden with a 20 foot perimeter. They enlarged their garden
to be twice as long and three feet wider than it was originally. They had to, since their tomato
plants were getting out of control. The enlarged garden has a 40 foot perimeter. What were the
dimensions of the original garden?
Make a sketch:
Define the variables:
Write an equation for the perimeter of the original garden.
Write an equation for the perimeter of the enlarged garden.
Solve the system and answer the question.
4-20 One Equation or Two Equations?
Example 5. Elise took all of her cans and bottles from home to the recycling plant. The number of cans was one
more than four times the number of bottles. She earned 12¢ for each bottle and 10¢ for each can, and ended up
earning $2.18 in all. How many cans and bottles did she recycle?
Part a. Elise decided to solve the problem by writing 1equation with 1 variable. She wrote:
Let b = for the # of bottles.
Her equation was 12b + 10(4b + 1) = 218.
(How did $2.18 become 218?)
Solve her equation. How many bottles did she have?
How many cans?
Part b. Her friend Marcus thought this would be easier to answer with 2 equations and 2 variables.
He wrote:
Let b = the # of bottles,
c = the # of cans.
His equations were c = 4b + 1 and 12b + 10c = 218.
Solve the systems of equations.
Did you get the same number of bottles and cans?
 Practice: On your own note book paper, write and solve each system.
For credit – all work must be shown including the ‘Let’ statements for the variables.
1. 20,000 tickets were sold to the Green Day concert. Stage level seats cost $105 and higher level seats cost $75.
If the total money collected from selling tickets was $1,740,000, how many tickets of each type were sold?
Define the variables: Let x =
y=
Write an equation showing 20,000 tickets were sold.
Write an equation showing $1,740,000 in ticket sales.
Solve the system of equations and answer the question.
2. There are 21 animals on Farmer Cole’s farm – all sheep and chickens. If the animals have a total of 56 legs,
how many of each type of animal lives on his farm?
3. An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are
worth five points. How many two point questions are on the test? How many five point questions are on the
test? How many 2 point questions are on the test?
4. Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small
pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
5. The Lakers scored a total of 80 points in a basketball game against the Bulls. The Lakers made a total of 37
2-point and 3-point baskets. How many 2-point shots did the Lakers make? How many 3-point shots did the
Lakers make?
6. The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the
numbers. (tip: look at Example 5 Part b. )
7. Brodie’s Gourmet Pretzel Shop specializes in selling the very finest chocolate covered pretzels. Banky
bought 4 white chocolate pretzels and 6 dark chocolate pretzels for $10.50. Holden bought 8 white
chocolate and 3 dark chocolate pretzels for $9.75. What is the cost of each type of pretzel?
8. Suppose you invested $10,000, part at 6% annual interest and the rest at 9% annual interest. (How do you
convert 6% and 9% to decimal values?) If you received a total of $684 in interest after one year, how much
did you invest at each rate?
9. Tyler is catering a banquet for 250 people. Each person will be served either a chicken dish that costs $5
each or a beef dish that costs $7 each. Tyler spent $1500. How many dishes of each type did Tyler serve?
10. Your teacher is giving you a test worth 100 points containing 40 questions. There are two-point and fourpoint questions on the test. How many of each type of question are on the test?
11. The math club and the science club had fundraisers to buy supplies for a hospice. The math club spent $135
buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of
juice and two cases of bottled water. How much did a case of juice cost? How much did a case of bottled
water cost?
12. Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later, you
bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much
did each party hat cost?