5-3C Word Problems (Class Work) Alg 1CP

“Solving Word Problems with Linear Systems by Using Substitution” (PowerPoint)

Solve these word problems by defining 2 different variables and writing 2 equations. Then, use substitution or elimination to solve each system.

EXAMPLE: Jenny has 8 moving boxes that she can use to pack for college. Each box can hold 15 pounds of clothing or 60 pounds of books. If Jenny is moving 255 pounds how many boxes of each type are there?

Define Variables: Number Let c = number of clothes boxes Let b = number of book boxes

Define Variables: Weight Let 15c = weight of clothing boxes Let 60b = weight of book boxes

Verbal Model: number # of clothing boxes + # of book boxes = total # of boxes

Equation: number c + b = 8

Verbal model: weight weight of clothing boxes + weight of book boxes = total weight

Equation: weight 15c + 60b = 255

Solve. c + b = 8 15c + 60b = 255

Solution: 3 book boxes and 5 clothing boxes.

#1 In one day the museum collected $1590 from 321 people. The price of admission is $6 for an adult and $4 for a child. How many adults and how many children were admitted to the museum?

Define Variables: Number ___________________________________________________________

Define Variables: Value ___________________________________________________________

Verbal Model: number __________________________________________________________

Equation: number _________________________________________

Verbal model: value __________________________________________________________

Equation: value __________________________________________

Solve.

Solution:________________________________________

#2 An investor bought 225 shares of stock. Stock A was purchased at $50 per share and Stock B at $75 per share. If $13,750 worth of stock was purchased, how many shares of each kind of stock did the investor buy?

Define Variables: Number ___________________________________________________________

Define Variables: Value ___________________________________________________________

Verbal Model: number __________________________________________________________

Equation: number ____________________________________________________

Verbal model: value __________________________________________________________

Equation: value ____________________________________________________

Solve.

Solution:________________________________________

# 3 The length of a rectangle is 1 m more than twice its width. If the perimeter is 110 meters, find the dimensions.

Define Variables: _________________________________________________________________

Verbal Model: _________________________________________________________________

Equation ____________________________________________________

Verbal Model: Perimeter _______________________________________________________

Equation: Perimeter ________________________________________________

Solve.

Solution:________________________________________

Complete the following problems in your spiral. Use the same format as the examples. Practice 1 A sightseeing boat charges $5 for children and $8 for adults. On its first trip of the day, it collected $439 for 71 paying passengers. How many children and how many adults were there?

Practice 2 The length of a rectangle is 12 inches more than twice its width. If the perimeter is 90 inches, what are the dimensions of the rectangle?

5-3C Wkst Alg 1CP