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 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: (-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

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 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.

Let x, x+1, x + 2 be the measures of the angles Equation: x + x x + 2 = 180˚ 3x + 3 = 180 ˚ 3x = 177 x = 59 Therefore the measures of the angles are 59˚, 60˚ and 61˚. Check: = 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 Equation: w + 2w + w + 2 w = 66 6w = 66 w = 11 Therefore the width is 11ft and the length is 22ft Perimeter = 66ft w 2w

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 x – 5 = 50 3x + 5 = 50 3x = 45 x = 15 Therefore, the pieces are: 10, 15 and 25 inches