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2.6 Applications

2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

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Page 1: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

2.6 Applications

Page 2: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

6 steps to solve a word problem

• Read and underline important terms

• Assign a variable

• Write an equation

• Solve equation

• Check answer

• State answer

Page 3: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

• Consecutive integers:

x, x+1, x+2, x+3, …

• Even or odd consecutive integers:

x, x+2, x+4, x+6, …

Page 4: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Ex1) Find two consecutive integers whose sum = -45

Page 5: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Ex1: Find two consecutive integers whose sum = -45

Let x and x + 1 be the two consecutive integers

Equation: x + x + 1 = -45

2x + 1 = -45

2x = - 46

x = -23

Therefore the two consecutive integers are

-23 and -22

Check: -23 + (-22) = -45 Correct

Page 6: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Practice

1) Find 3 consecutive integers whose sum = 33

Page 7: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Practice

2) Find two consecutive odd integers whose sum = -32

Page 8: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Practice

3) Find four consecutive even integers whose sum = 36

Page 9: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Practice

4) The ages of Tim, Tom, and Ty are consecutive integers. The sum of their ages is 108. What are their ages?

Page 10: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Ex2) Find two consecutive even integers such that six times the smaller added to the larger give a sum of 86

Page 11: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Ex2) Find two consecutive even integers such that six times the smaller added to the larger give a sum of 86

Let x and x + 2 be two consecutive even integers

Equation: 6x + (x+2) = 86

7x + 2 = 86

7x = 84

x = 12

Therefore the two consecutive even integers are 12 and 14

Check: 6(12) + 14 = 86

72 + 14 =86 Correct

Page 12: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

• Degree: used to measure angles

• Sum of the angles inside any triangle is 180 degree

Page 13: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

ex3) In a triangle, one angle is 1 degree more than the smallest angle, and another angle is 2 degrees more than the smallest angle. Find the measurement of the angles.

Page 14: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

ex3) In a triangle, one angle is 1 degree more than the smallest angle, and another angle is 2 degrees more than the smallest angle. Find the measurement of the angles.

• Let x, x+1, x + 2 be the measures of the angles• Equation: x + x + 1 + x + 2 = 180˚ 3x + 3 = 180 ˚ 3x = 177 x = 59• Therefore the measures of the angles are 59˚,

60˚ and 61˚.• Check: 59 + 60 + 61 = 180 ˚

Page 15: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

Practice

In a triangle, one angle is 50 degree more than the smallest angle, and the other angle is three times the smallest angle. Find the measurement of the angles.

Page 16: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

ex4) The length of a rectangular floor is twice the width. Find its dimension if you know the floor’s perimeter is 66ft

Page 17: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

4) The length of a rectangular floor is twice the width. Find its dimension if you know the floor’s perimeter is 66ft

• Draw picture and set up variable

• Equation: w + 2w + w + 2 w = 66 6w = 66 w = 11Therefore the width is 11ft and the length is 22ft

Perimeter = 66ft w

2w

Page 18: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

ex5) A piece of pipe is 50 in. long. It is cut into three pieces. The longest piece is 10in. more than the middle-sized piece, and the shortest piece measures 5 in. less than the middle-sized piece. Find the lengths of the three pieces.

Page 19: 2.6 Applications. 6 steps to solve a word problem Read and underline important terms Assign a variable Write an equation Solve equation Check answer State

ex5) A piece of pipe is 50 in long. It is cut into three pieces. The longest piece is 10in. more than the middle-sized piece, and the shortest piece measures 5 in. less than the middle-sized piece. Find the lengths of the three pieces.

Let x be the length of the middle-sized pieceThen x + 10 is the length of the longest pieceAnd x – 5 is the length of the shortest piece x + x + 10 + x – 5 = 50 3x + 5 = 50 3x = 45 x = 15Therefore, the pieces are: 10, 15 and 25 inches