Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
Name: ___________________________
Section 5a Notes
Find the solution to each system.
1.)
3x – 4 = y
2.)
2x – 3y = -9
x + y = 12
x = 2y – 3
Set up a system of equations. Then solve
1. Cara had a combined total of 64 hits during her junior and senior years of fast
pitch softball. In her senior year, Cara had 5 fewer than twice as many hits as her
junior year. How many hits did Cara have in her senior year?
(1) Identify and define the variables.
(2) Set up two equations. Look for totals.
(3) Solve the system using substitution or elimination.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
2. The schoolyard has 12 trees. The number of maple trees is 3 less than twice the
number of pine trees.
A.
B.
C.
D.
There are 7 pine trees and 5 maple trees.
There are 2 more pine trees than maple trees.
There are 2 more maple trees than pine trees.
There are 6 pine trees and 6 maple trees.
3. The perimeter of a rectangle deck is 175 feet. The length of the deck, L, is 6 feet
longer than 2 times the width, W. Which system of equations can be solved to
determine the length and width, in feet, of the deck? (Hint: The formula for the
perimeter of a rectangle is P = 2L + 2W.)
A. 2L+ 2W = 175
L = 2 – 2W
B. 2L + 2W = 175
L = 2W – 6
C. 2L + 2W = 175
L = 6 – 2W
D. 2L + 2W = 175
L = 6 + 2W
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
Section 5a PRACTICE
1. Solve the system.
y=x+5
2y – x = 13
2. The Mendez family is going to see a play. Adult tickets cost $9 and children’s
tickets cost $6. There are 6 people in the family, and they spend a total of $48 on
tickets. Which system of equations can be solved to determine a, the number of
adult tickets, and c, the number of children’s tickets?
A. 9a + 6c = 48
a+c=6
C. 6a + 9c = 48
a+c=9
B. 9a + 6c = 48
a–c=6
D. 6a + 9c = 48
a–c=6
3. The perimeter of a rectangle deck is 175 feet. The length of the deck, L, is 6 feet
longer than 2 times the width, W. This can be represented by the system of
equations given below. Which of the following statements are true?
L = 6 + 2W
2L + 2W = 175
A. W = 27.1 feet, L = 60.1 feet
1
1
6
1
3
1
3
6
B. W = 27 feet, L = 60 feet
C. W = 60 feet, L = 27 feet
D. None of these are true because I got a decimal.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
Section 5b Notes
Use Elimination to solve the following systems.
1.)
x + y = 12
x–y=8
2.)
x + y = 14
3x – 2y = 2
3.) The sum of two numbers is 27. Their difference is 5. Find the numbers.
4.) On a cross-country team, there are 14 athletes. Three times the number of males is 2
more than twice the number of females. How many females are on the team?
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
5.) Mr. Webster is selling tickets to a play. On the first day of ticket sales the school sold
1 senior ticket and 3 student tickets for a total of $42. The school took in $57 on the
second day by selling 2 senior tickets and 3 student tickets. This can be modeled by the
system given below, where r is the price of a senior ticket and t is the price of a student
ticket.
r + 3t = 42
2r + 3t = 57
Which of the following are true?
A.
B.
C.
D.
Mr. Webster sold 15 senior tickets and 9 student tickets.
The price of a student ticket is $15 and the price of a senior ticket is $9.
The price of a student ticket is $9 and the price of a senior ticket is $15.
We do not know how much each ticket costs.
6.) At the farm market, Jed bought 4 lbs. of apples and 6 lbs. of peaches for $18. Maria
bought 2 lbs. of apples and 10 lbs. of peaches for $23. If a is the price per pound for
apples and p is the price per pound for peaches, answer the following questions.
A. Write a system of equations that models the situation given above.
B. Solve the system to determine which of the following statements are true.
A.
B.
C.
D.
Peaches weigh more than apples.
Jed bought more peaches than apples.
Apples cost more than peaches.
Peaches cost more than apples.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
Unit 2 Section 5b Homework
Set up equations and solve the system of equation. Show work.
1. The sum of two numbers is 92. Their difference is 20. Find the numbers.
2. The sum of two numbers is 90. Their difference is 18. Find the numbers.
3. At the Pizza Palace, the total price for 5 large pizzas plus 2 medium pizzas is
$81.50. The total for 4 large pizzas plus 3 medium pizzas is $78.50? Set up a
system of equations then determine how much each type of pizza costs.
(1) Define the variables.
(2) Set up a system of equations.
(3) Solve the system for each missing piece.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
4. Mike and Val each improved their yards by planting rose bushes, r, and shrubs, s.
They bought their supplies from the same store. Mike spent $82.50 on 4 rose
bushes and 7 shrubs. Val spent $50 on 4 rose bushes and 2 shrubs. This can be
modeled by the system below.
4r + 7s= 82.50
4r + 2s = 50
A.
B.
C.
D.
A rose bush costs $2.75 more than a shrub.
A rose bush costs $6.50.
A shrub costs more than a rose bush.
Val bought more shrubs than Mike.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
Section 5 Practice
Use systems of equations to solve each problem. Show all work.
1. Michelle is making goodie bags for Christmas filled with chocolates and
strawberries. Chocolates cost $2.50 per lb. and strawberries $3.00 per lb. Michelle
bought 15 pounds of chocolate and strawberries and spent $40.
a. Define the two variables represented in this problem.
b. Write an equation showing that Michelle spent a total of $40 on chocolates and
strawberries.
c. Write an equation showing that Michelle bought a total of 15 lbs. of chocolates
and strawberries.
d. Solve the system of equations to find out how many lbs. of chocolate and how
many lbs. of strawberries Michelle bought.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
For questions 2 - 4 use the following information.
Tori spent $1,500 on a banquet that she is catering for 250 people. Each person will be
served either a chicken dish that costs $5 each or a beef dish that costs $7 each.
2. Which system represents the situation presented above?
A.) 5B + 7C = 1500
C + B = 250
B.) 5C + 7B = 1500
C + B = 250
C.) C + B = 1500
5C + 7B = 250
D.) 250C + 1500D = 5
C+B=7
3. To solve this system using elimination, what would be a logical first step to
completing the problem?
A.
B.
C.
D.
Multiply one equation by 5
Divide one equation by -5
Multiply one equation by -5
Multiply one equation by 7
4. How many chicken dishes will be served?
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
5. Brodie’s Gourmet Pretzel Shop specializes in selling the very finest chocolate
covered pretzels. Sally bought 4 white chocolate pretzels and 6 dark chocolate
pretzels for $10.50. Maggie bought 8 white chocolate and 3 dark chocolate
pretzels for $9.75. Use the system of equations given below where w is the price
of a white chocolate pretzel and d is the price of a dark chocolate pretzel.
4w + 6d = 10.50
8w + 3d = 9.75
Based on the information above, which of the following statements are true?
A. White and dark chocolate pretzels cost the same.
B. White chocolate pretzels cost more than dark chocolate pretzels.
C. Sally bought more pretzels than Maggie.
D. Dark chocolate pretzels cost more than white chocolate pretzels.
Algebra 1B
UNIT 2: Part 3- Applications of Solving Systems of Equations
6. Your teacher is giving you a test worth 100 points containing 40 questions. There
are two-point and four-point questions on the test. How many of each type of
question are on the test?
a. Define the unknown variables in this problem.
b. Write an equation showing how many questions are on the test.
c. Write an equation showing the questions on the test are worth 100.
d. Solve the system of equations to find how many of each type of question are on
the test.