1.3 Applications

Increased by + Difference of - Quotient of ÷ Less than - Of x Ratio ÷ Add, Subtract, Multiply, or Divide Increased by + Difference of - Quotient of ÷ Less than - Of x Ratio ÷ Product of x Sum of + Decreased by - twice x

Degree: unit used to measure angles Sum of the angles inside any triangle is 180 degree Consecutive integers: x, x+1, x+2, x+3, … Even or odd consecutive integers: x, x+2, x+4, x+6, …

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

Find the speed of a man who runs 100 meters in 9.87 seconds? Formula: d = r t

Find the speed of a man who runs 100 meters in 9.87 seconds? Formula: d = r t d / t = r 100/9.87 = r 10.13 = r So, the man’s speed is 10.13 meters per second

2) The length of a rectangular floor is twice the width 2) The length of a rectangular floor is twice the width. Find its dimensions if you know the floor’s perimeter is 66ft

Draw picture and set up variable 2) The length of a rectangular floor is twice the width. Find its dimensions 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 2w Perimeter = 66ft w

3) Tim left a 25% tip on a meal. Including the tip, its cost was $50 3) Tim left a 25% tip on a meal. Including the tip, its cost was $50. What was the cost of the meal before the tip?

3) Tim left a 25% tip on a meal. Including the tip, its cost was $50 3) Tim left a 25% tip on a meal. Including the tip, its cost was $50. What was the cost of the meal before the tip? Let x be the cost of the meal Equation: x + 0.25x = 50 1.25x = 50 x = 40 Therefore the cost of the meal is 40 dollars

4) A piece of pipe is 50 in. long. It is cut into three pieces 4) A piece of pipe is 50 in. long. It is cut into three pieces. The longest piece is 10 inches more than the middle-sized piece, and the shortest piece measures 5 inches less than the middle-sized piece. Find the lengths of the three pieces.

4) A piece of pipe is 50 in long. It is cut into three pieces 4) 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

5) 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 5) 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

6) 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.

6) 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 ˚

7) At a certain real estate firm, realtors selling homes receive a commission of:7% for the first $100,000 of the selling price, and 3% for any amount exceeding $100,000. A realtor for the firm received $15,000 for selling a house. What was its selling price?

7) At a certain real estate firm, realtors selling homes receive a commission of:7% for the first $100,000 of the selling price, and 3% for any amount exceeding $100,000. A realtor for the firm received $15,000 for selling a house. What was its selling price? With a $100,000 house, the realtor will receive 0.07 (100,000) = $7000 Let x be the selling price Equation: 0.07(100,000) + 0.03(x-100,000)=15,000 7000 + .03x - 3000= 15,000 4000 + .03x = 15,000 .03x = 11,000 x = $366,666.67 So the selling price is $366,666.67

8) A moving side-walk in Saigon airport is 300 ft long and moves at the speed of 6 ft/sec. If Tim walks at a speed of 4 ft/sec, how long will it take him to travel the 300 ft using the moving sidewalk? d = r t t = d/r = 300 / (6+4) = 30 It will take Tim 30 seconds to travel.

9) A canoe moves at a rate of 7km/h in still water 9) A canoe moves at a rate of 7km/h in still water. How long will it take the canoe to travel 16km downriver (with the current) if the current moves at a rate of 1 km/h d = r t t = d/r = 16 / (7+1) = 2 It will take the canoe 2 hours to travel downriver.

10) Chris swims at a speed of 2mph in still water 10) Chris swims at a speed of 2mph in still water. The current in a river is moving at 0.5mph. How long will it take Chris to swim 0.3 mile upriver against the current? d = r t t = d/r = 0.3 / (2-0.5) = 0.3 / 1.5 = 0.2 hour It will take Chris 12 minutes to travel.