Name
Class
Lesson 5-4 Date
Systems in the Real World
Lesson Objective
Common Core State Standards
To use systems of linear equations to solve
real-world problems
Expressions and Equations: 8.EE.8.b, 8.EE.8.c
Examples
Write a system of equations to represent the situation.
number of days
cost
Let x 5____________________
and y 5 _ total
__________________
.
Main Street: y 5 30 1 2.5x
High Street: y 5 40 1 1.5x
Graph both equations.
The lines appear to intersect at  10 ,  55 .
less than 10 days.
High Street Garage is less expensive for more than 10 days.
The cost is the same for 10 days.
y
50
40
30
20
10
0
2
4
6
Days
8
x
10
Main Street Garage is less expensive for
2 Application: Money Tina has 50 coins, all dimes and quarters.
The value of the coins is $7.10. Write a system of equations to
determine how many dimes and how many quarters Tina has.
Write a system of equations to represent the situation.
number of dimes
number of quarters .
Let d 5________________________
and d 5 _____________________
← The number of dimes and quarters as an equation
d 1 q 5 50
0.10d 1
Use the substitution method to solve the system. Check your solution.
d 5 36 q 5 14
So, Tina has 36 dimes and 14 quarters.
0.10(50 2 q) 1 0.25q 5 7.10
5 2 0.1q 1 0.25q 5 7.10
0.15q 5 2.10
q 5 14
d 5 50 2 q 5 50 2 14 5 36
50
441198_C3_Ch5_WKbk_Ver-1.indd 50
0.25 q
5 7.10 ← The values of the dimes and the quarters as an equation
Course 3 Lesson 5-4
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
60
Cost (dollars)
$30.00 monthly fee plus $2.50 per day. The High Street Garage
charges a $40.00 monthly fee plus $1.50 per day. ­Determine
when it would be better to park in the Main Street garage,
and when it would be better to park in the High Street garage.
All rights reserved.
1 Application: Fees The Main Street Parking Garage charges a
Daily Notetaking Guide
10/10/12 3:52 PM
Name
Class
Date
pplication: Dining Kevin and Rose went to a deli to have lunch with
3 A
their friends. The people at Kevin’s table ordered 3 salads and 2 cups of
soup and paid $15.45. The people at Rose’s table ordered 3 salads and 4 cups of soup and paid $21.03. Determine the cost of each salad and
each cup of soup.
Write a system of equations to represent the situation.
Let s 5 cost of a salad
All rights reserved.
15.45
3? s 12? c 5
3 ? s 1 4 ? c 5 21.03
and c 5 cost of a cup of soup .
← The order from Kevin’s table as an equation
← The order from Rose’s table as an equation
Make additive inverses. Multiply each side of either equation by
Use the elimination method to solve the system of equations.
s5
3.29
c5
21 .
2.79
23s 2 2c 5 215.45
3s 1 4c 5 21.03
2c 5 5.58
c 5 2.79
3s 1 2(2.79) 5 5.45
s 5 3.29
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
So, each salad costs $3.29 and each cup of soup costs $2.79 .
Quick Check
1. Alexa is trying to decide between two hotels. Hotel A charges $80 per night. Hotel B charges $70 per night plus a one-time parking fee of $20. Which hotel should she choose? Explain your reasoning.
She should choose Hotel A if she is staying more than 2 nights, and
Hotel B if she is staying less than 2 nights. The cost is the same for
2 nights.
2. Alyssa has a collection of 35 character figures. Some of the figures cost $10 each and the others cost $25 each. The total value of her figures is $575. Write and solve a system of equations to find how many $10 figures and how many $25 figures she has.
p 1 q 5 35; 10p 1 25q 5 575 Twenty $10 figures and fifteen $25 figures
3. Ji downloaded 15 songs and 3 movies for $32.25. Arie downloaded 22 songs and 3 movies for $41. What is the cost of downloading one movie?
$4.50
Daily Notetaking Guide
441198_C3_Ch5_WKbk_Ver-1.indd 51
Course 3 Lesson 5-4
51
10/12/12 12:40 PM