1. 3 Applications
Add, Subtract, Multiply, or Divide Increased by Difference of Quotient of Less than Of Ratio Product of Sum of Decreased by twice + ÷ x + 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
1) 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. Find its dimension if you know the floor’s perimeter is 66 ft • Draw picture and set up variable 2 w Perimeter = 66 ft w • Equation: w + 2 w + 2 w = 66 6 w = 66 w = 11 Therefore the width is 11 ft and the length is 22 ft
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. 25 x = 50 1. 25 x = 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. The longest piece is 10 inches more than the middle-sized piece, and the shortest piece measures 5 inches less than the middlesized piece. Find the lengths of the three pieces.
4) A piece of pipe is 50 in long. It is cut into three pieces. The longest piece is 10 in. more than the middlesized 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 + 10 + x – 5 = 50 3 x + 5 = 50 3 x = 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
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: 6 x + (x+2) = 86 7 x + 2 = 86 7 x = 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. • Let x, x+1, x + 2 be the measures of the angles • Equation: x + 1 + x + 2 = 180˚ 3 x + 3 = 180 ˚ 3 x = 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? • 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 +. 03 x - 3000= 15, 000 4000 +. 03 x = 15, 000. 03 x = 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=rt t = d/r = 300 / (6+4) = 30 It will take Tim 30 seconds to travel.
9) A canoe moves at a rate of 7 km/h in still water. How long will it take the canoe to travel 16 km downriver (with the current) if the current moves at a rate of 1 km/h d=rt t = d/r = 16 / (7+1) = 2 It will take the canoe 2 hours to travel downriver.
10) Chris swims at a speed of 2 mph in still water. The current in a river is moving at 0. 5 mph. How long will it take Chris to swim 0. 3 mile upriver against the current? d=rt t = d/r = 0. 3 / (2 -0. 5) = 0. 3 / 1. 5 = 0. 2 hour It will take Chris 12 minutes to travel.
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