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Setting up and Solving Problems. The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?. What is the length of the rectangle?. What is the question we need to answer?.

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Presentation Transcript
slide2

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

What is the length of the rectangle?

What is the question we need to answer?

slide3

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

Define the variable.

Since the length is 6 more than the width let w = width

slide4

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

If w= width, how would you write the length?

The length is 6 more than the width length = w + 6

Write the length in terms of the width.

slide5

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

width = w

Draw a picture to help you visualize this problem.

length = w + 6

w + 6

w

w

w + 6

slide6

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

Is there any other important information that we need in order to solve this problem?

The perimeter is equal to 24 inches.

What does that mean?

slide7

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

Write the equation that will be used to solve this problem.

w + 6

w

w

w + 6

+

w

w

w + 6

w + 6

+

+

= 24

slide8

The length of a rectangle is 6 more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

Combine Like Terms

w + 6 + w + 6 + w + w = 24

4w + 12 = 24

Subtract 12 from both sides.

- 12 -12

4w = 12

4w = 12

Divide both sides by 4.

4 = 4

w= 3

What does that mean?

slide9

The length of a rectangular-shaped garden is four times the width. The perimeter is 100 feet. What are the dimensions of the garden?

slide10

The sum of three numbers is 180. One number is twice the first, and another number is triple the first. What are the three numbers?

slide11

The width of a rectangle is 2 cm less than its length. The perimeter is 16 cm. What is the length of the rectangle?

slide12

A camera manufacturer spends $2100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. How many cameras must the company sell in one day to equal its daily cost?

slide13

Summarize steps we have used to solve real world problems.

  • Name the Question you are answering.
  • Define the variable.
  • List important information and their relationships.
  • Draw a picture.
  • Write an equation with one variable.
  • Solve the equation.
  • Check your answer. Does it answer the question?
  • Write a statement to answer the question.