MAT 150 Unit 5

1
MAT 150 Unit 5

• Ch 7 3
• Word Problems

2
Section 7 3 Word Problems

• A farmer marks off a 32 m wide rectangular plot
  with 158 m of fencing. What is the length of the
  plot?

3
Section 7 3 Word Problems

• Strategy for solving
• Read the problem carefully.
• Understand all the words in the problem.
• Draw a diagram if appropriate.
• What are you asked to find?
• Assign a variable to the unknown.
• What is given?
• What is the stated or implied relationship?
• Write a symbolic equation to describe the
  relationship.
• Solve and check. Express answer in terms of
  problem.

4
Section 7 3 Word Problems

• A farmer marks off a 32 m wide rectangular plot
  with 158 m of fencing. What is the length of the
  plot?
• Read carefully
• Understand all the words
• Draw a diagram if appropriate
• 32 m
• length
• What are you asked to find? Assign a variable
  to the unknown
• The length, L length
• What is given?
• Rectangular plot, 32 m wide, 158 m total of fence
• What is the stated or implied relationship?
• Fencing will be used to go around the perimeter
  of the lot
• Write a symbolic equation to describe the
  relationship.
• P L W L W or 2L 2W
• 158 2L 2(32)
• Solve and check. Express answer in terms of
  problem.

5
Section 7 3 Word Problems

• Solve and check.
• 158 2L 2(32)
• 158 2L 64
• 64 64
• 94 2L
• 2 2
• 47 L therefore the length of the plot is 47
  m

6
Section 7 3 Word Problems

• A machine part weighs 2.7 kg and is to be shipped
  in a box. If the total weight of 3 packaged
  machine parts is 9.3 kg, how much does each box
  weigh?

7
Section 7 3Word Problems

• A machine part weighs 2.7 kg and is to be shipped
  in a box. If the total weight of 3 packaged
  machine parts is 9.3 kg, how much does each box
  weigh?
• 4UNKNOWN weight of a box, b wt of box
• 5 GIVEN each machine part is 2.7 kg, total
  weight is 9.3 kg
• 7 RELATIONSHIP total weight is 3 parts and
  boxes
• 8 EQUATION 9.3 3(2.7 b) or 9.3 2.7 b
  2.7 b 2.7 b
• 9 SOLUTION 9.3 3(2.7 b)
• 9.3 8.1 3b
• 8.1 8.1
• 1.2 3b
• 3 3
• .4 b, therefore
  each box weighs .4 kg

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Section 7 3 Word Problems

• Bill was taken to lunch by a friend. The order
  included a 12 inch turkey sub, a 6 inch turkey
  sub and two sweet teas. Bill didnt notice the
  price of the subs but did recall that the 12 in.
  sub cost 1.50 more than the 6 in. sub. And the
  tea cost 1.25 each. If lunch cost 10, how much
  did each sub cost?

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Section 7 3Word Problems

• Bill was taken to lunch by a friend. The order
  included a 12 inch turkey sub, a 6 inch turkey
  sub and two sweet teas. Bill didnt notice the
  price of the subs but did recall that the 12 in.
  sub cost 1.50 more than the 6 in. sub. And the
  tea cost 1.25 each. If lunch cost 10, how much
  did each sub cost?
• 4UNKNOWN cost of each sub
• 5 GIVEN total bill is 10, each tea was
  1.25, large sub was 1.50 more than small
• Therefore small sub x, large
  sub x 1.50
• 7 RELATIONSHIP total order was 1 lg sub 1 sm
  sub 2 tea 10
• 8 EQUATION (x 1.50) x 2(1.25) 10
• 9 SOLUTION (x 1.50) x 2(1.25) 10
• (x 1.50) x
  2.50 10
• 2x 4 10
• - 4 - 4
• 2x 6
• 2 2
• x 3
  so the small sub was 3.00 and the large 4.50

10
Section 7 3 Word Problems

• A student purchased a new math textbook, a used
  history textbook, and a notebook. His receipt
  was for 189 plus tax. He knew that the math
  text cost twice as much as the history book and
  notebook combined. If the notebook cost 3, how
  much was each text book?

11
Section 7 3 Word Problems

• A student purchased a new math textbook, a used
  history textbook, and a notebook. His receipt
  was for 189 plus tax. He knew that the math
  text cost twice as much as the history book and
  notebook combined. If the notebook cost 3, how
  much was each text book?
• 4UNKNOWN cost of each book
• 5 GIVEN total bill is 198, notebook was 3,
  math book twice notebook and history book
  combined
• Therefore
  history x, math 2(x 3)
• 7 RELATIONSHIP total order was 1 math book 1
  history book 1 notebook 198
• 8 EQUATION 2(x 3) x 3 198
• 9 SOLUTION 2(x 3) x 3 198
• 2x 6 x 3
  198
• 3x 9 198
• - 9 - 9
• 3x 189
• 3 3
• x 63, therefore the history book cost 63,
  the math book cost 2(63 3) 2(66) 132