Business Math

Business Math

Find x if 5x+10=20

Workshop 39

Objectives

• Solve linear combinations algebraically

• Add and subtract two equations

• Express one unknown in terms of the other

Steps for solving

There are many applications that result in two equations with two unknowns that need to be solved. Such systems are identified as linear

combinations and are solved, algebraically, in this method:

Eliminate one of the variables by adding or subtracting the two equations.

Then solve the resulting equation in one unknown. Substitute the solution into one of the original equations to find the value of the other variable.

Open Ended

Example 1

At the starting point of the 30 k Cycle Run there were a total of 50

cycles. Some were tricycles (3 wheels) while most were bicycles (2

wheels). The equipment counted just the wheels and found a total of

107 wheels. How many bicycles were there? How many tricycles were

there?

Answer

Step 1: Identify the unknowns.

Let B = the number of Bicycles (2B wheels)

Let T = the number of Tricycles (3T wheels)

Step 2: Write the equations.

B + T = 50

2B + 3T = 107

Multiply the fi rst equation by 3 3B + 3T = 150

Subtract the second equation from the fi rst 2B + 3T = 107

B = 43

Now substitute 43 for B in the fi rst equation: 43 + T = 50

Therefore T = 7

There were 43 bicycles and 7 tricycles.

Open Ended

Activity 1

At the starting point of the 30 k Cycle Run there were a total of 40

cycles. Some were tricycles (3 wheels) while most were bicycles (2

wheels). The equipment counted just the wheels and found a total of

91 wheels. How many bicycles were there? How many tricycles were

there?

Open Ended

How can you check your answers?

Open Ended

Activity 2

Solve the equation

5v − 4w = 189

2v + 5w = 201

12p + 5q = 63

9p + 7q = 57

Open Ended

Why do you add or subtract the equations?

Open Ended

Activity 3

The length of a rectangle is twice the width and the perimeter of the rectangle is 42 feet. After finding the width and the length, find the area of the rectangle

Open Ended

Activity 3

On Friday the corner newsstand sold 5 more copies of The New York

Times than it did copies of The Washington Post. If the newsstand sold

59 copies of The New York Times and The Washington Post combined,

how many of each was sold?

Open Ended

Activity 3

If there are twice as many girls as boys in fourth period English and

there are 33 students in all, how many girls are in fourth period

English? How many boys?

Answer

Width = 7 feet; Length = 14 feet; Area = 98 square feet

32 copies of the New York Times and 27 copies of the Washington Post

22 girls and 11 boys

Plenary

Write the summary of the lesson.