2.6 Applications
6 steps to solve a word problem
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Read and underline important terms
Assign a variable
Write an equation
Solve equation
Check answer
State answer
• Consecutive integers:
x, x+1, x+2, x+3, …
• Even or odd consecutive integers:
x, x+2, x+4, x+6, …
Ex1) Find two consecutive integers whose sum = -45
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
Practice
1) Find 3 consecutive integers whose sum =
33
Practice
2) Find two consecutive odd integers whose
sum = -32
Practice
3) Find four consecutive even integers whose
sum = 36
Practice
4) The ages of Tim, Tom, and Ty are
consecutive integers. The sum of their ages
is 108. What are their ages?
Ex2) Find two consecutive even integers such that
six times the smaller added to the larger give a
sum of 86
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
• Degree: used to measure angles
• Sum of the angles inside any triangle is
180 degree
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.
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 ˚
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.
ex4) The length of a rectangular floor is
twice the width. Find its dimension if you
know the floor’s perimeter is 66ft
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
2w
Perimeter = 66ft
w
• Equation:
w + 2w + w + 2 w = 66
6w
= 66
w
= 11
Therefore the width is 11ft and the length is 22ft
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.
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 piece
Then x + 10 is the length of the longest piece
And x – 5 is the length of the shortest piece
x + x + 10 + x – 5 = 50
3x + 5
= 50
3x
= 45
x
= 15
Therefore, the pieces are: 10, 15 and 25 inches