Lesson 3.12: Modeling with Linear Systems

Question 1

Which system of equations models this problem?

Revolt · Accepted Answer

d = 56td = 60t – 2

Question 2

What is the original number described in the word problem?

Revolt · Accepted Answer

45

Question 3

Which system models this problem?

Revolt · Accepted Answer

x + y < 50

Question 4

The solution can be expressed as (8, 9, 11)✔ (11, 9, 8)(9, 8, 11).

Revolt · Accepted Answer

✔ (11, 9, 8)

Question 5

Let x = price of a standard ticket, y = price of a matinee ticket, and z = price of a senior ticket. 150x + 80y + 12z = 2,466380x + 95y + 48z = 5,419210x + 130y + 60z = 3,960 220x + 225y = 4,445540x + 270y = 8,370 → y = −2x + 31 x = 11

Revolt · Accepted Answer

8

Question 6

The solutions to the system mean:

Revolt · Accepted Answer

The price of a standard ticket is $11. The price of a matinee ticket is $9. The price of a senior ticket is $8.

Question 7

Does a two-digit number exist such that the digits sum to 9 and when the digits are reversed the resulting number is 9 greater than the original number? Identify the system of equations that models the given scenario.

Revolt · Accepted Answer

t + u = 910t + u = 10u + t – 9

Question 8

The system on the left can be reduced to:t + u = 99t – 9u = –9Solving the system t= ⇒ 4, u= ⇒ 5.

Revolt · Accepted Answer

5

Question 9

Listed in order from smallest to largest, the numbers are ⇒ -2, ⇒ 5, and ⇒ 7.

Revolt · Accepted Answer

7

Question 10

z =

Revolt · Accepted Answer

8

Lesson 3.12: Modeling with Linear Systems Answers

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