1. 1.3 Applications

2. 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

3. 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, …

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

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

6. 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
= r
So, the man’s speed is meters per second

7. 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

8. 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

9. 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?

10. 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 x = 50
1.25x = 50
x = 40
Therefore the cost of the meal is 40 dollars

11. 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.

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

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

14. 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 = 86
7x = 84
x = 12
Therefore the two consecutive even integers are 12 and 14
Check: 6(12) + 14 = 86
=86 Correct

15. 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.

16. 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 x + 2 = 180˚
3x = 180 ˚
3x = 177
x = 59
Therefore the measures of the angles are 59˚, 60˚ and 61˚.
Check: = 180 ˚

17. 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?

18. 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) (x-100,000)=15,000
x = 15,000
x = 15,000
.03x = 11,000
x = $366,666.67
So the selling price is $366,666.67

19. 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.

20. 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.

21. 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.