7.
Gary goes to the grocery store to buy hot dogs and hamburgers for a cookout. He buys a total
of 8 packages for a total of $28.52. A package of hot dogs costs $2.29 and a package of
hamburgers costs $5.69.
Hot Dogs
Value
Amount
Hamburgers
MULTIPLE REPRESENTATIONS
For systems of linear inequalities that have only
whole number solutions, some students may choose
to display their answers in a table instead of as a
graph. Discuss factors that may make one
representation more desirable than the other.
Total
d
b
8
2.29d
5.69b
$28.52
d+b=8
2.29d + 5.69b = 28.52
8.
The sum of two numbers is 28, and the sum of 6 times the first number and 3 times the second number
is 105.
First Number
Second Number
Value
x
y
Total
28
Value
6x
3y
105
x + y = 28
6x + 3y = 105
Find a system of equations that corresponds to the situation and then solve the
resulting system.
9.
Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she
cancels her membership with the first gym and spends the rest of the year with the second gym. The
membership to the first gym costs $80 per month, while the membership for the second gym costs $45 per
month. If she ends up spending a total of $645 over the course of the year, how much time did she spend at
each gym?
80x + 45y = 645
x + y = 12
80x + 45y = 645
x + y = 12
+(-80x - 80y = -960)
____
-35y = -315
x + 9 = 12
10. John is selling tickets to an event. Attendees can either buy a general admission ticket or a VIP ticket. The
general adimission tickets are $70 and the VIP tickets are $105. If he knows he sold a total of 33 tickets and
made $2730, how many of each type did he sell?
70x + 105y = 2730
x + y = 33
70x + 105y = 2730
+(-70x - 70y = -2310)
____
35y = 420
x + y = 33
x + 12 = 33
y = 12
x = 21
© Houghton Mifflin Harcourt Publishing Company
x=3
y=9
So Jan spent 3 months at the first gym and 9 months at the second gym.
So John sold 21 general admission tickets and 12 VIP tickets.
Module 12
Exercise
IN1_MNLESE389755_U5M12L3 564
Lesson 3
564
Mathematical Practices
Depth of Knowledge (D.O.K.)
16
2 Skills/Concepts
MP.2 Reasoning
17–22
2 Skills/Concepts
MP.4 Modeling
23
2 Skills/Concepts
MP.4 Modeling
3 Strategic Thinking
MP.3 Logic
24–25
8/6/14 9:21 AM
Modeling with Linear Systems 564