Algebraic Expressions

• Consecutive numbers are numbers that follow each other continuously in order from smallest to largest. For example, 8, 9, 10, and 11 are consecutive numbers.
• Twice a number increased by five is 125. What is the number?

  A) Transposition

  B) 2x + 5 = 125

  C) 2x = -5 + 125

  D) x = 60

  
• When a number is increased by its reciprocal, the result is 2. Determine the number.

  A) x+1/x=2

  B) x(x + 1/x) = 2(x)

  C) x^2 - 2x + 1

  D) (x-1) (x-1)

  E) x = 1

  
• The sum of four consecutive positive whole numbers is 78. Determine the largest number among the consecutive numbers.

  A) x + (x+1) + (x+2) + (x+3)=78

  B) 4x+6=78

  C) 4x = -6 + 78

  D) x = 18

  E) 21

  
• Letty is three times as old as Bert. The sum of Bert’s and Letty’s ages is 48. How old is Letty?

  A) x+3x=48

  B) 4x=48

  C) x=12

  D) 36

  
• This year, Albert is 11 years older than Isaac. Three years ago, the sum of their ages was 67. Determine how old Isaac and Albert are this year.

  A) x - 3

  B) x + 8

  C) 67

  D) x + 11

  E) 2x+5=67

  F) 31

  G) 2x=62

  H) ALbert is 31 years old. Isaac is 42

  
• Five years from now, the sum of Richard’s age and Mike’s age will be 21. In the current year, Richard’s age is five years higher than twice Mike’s age. Determine Mike’s age in the present

  A) 2x+5

  B) x+5

  C) 2x+10

  D) 21

  
• formula for work problem

  A) time it takes B

  B) time it takes A

  C) time it takes for A and B

  D) 1

  E) 1

  F) 1

  
• Jacques can finish cleaning a garage in 2 hours. On the other hand, Kath can finish cleaning the same garage in 5 hours. Suppose Jacques and Kath work together to clean the same garage; how long would it take them to accomplish it?

  A) 2

  B) 5

  C) t

  D) 5t+2t=10

  E) 7t=10

  F) t=10/7

  
• There are two pipes in a large water tank: Pipe C and Pipe D. Pipe C puts water into the tank while Pipe D spills water. If only Pipe C is opened, it will fill the tank in 2 hours. Meanwhile,  if only Pipe D is opened, it will empty the tank in 3 hours. Suppose that for a particular purpose, both Pipe C and Pipe D are opened simultaneously; how many hours will it take for the tank to be full?

  A) 1/2 - 1/3 = 1/t

  B) 3t-2t=6

  C) t=6

  
• Distance Formula

  Distance = Rate x Time
• Cars A and B leave two different cities 400 km apart. Car A and B move toward each other at 60 and 50 kph, respectively. How many hours will it take for these two cars to meet or pass each other?

  A) 60t

  B) 50t

  C) 400

  D) 60t+50t=400

  E) 3.64

  
• Fred and Ludwig love cycling. One day they decided to test how long it would take to be 35 km apart if they started at a certain point and moved away from each other. Fred moves at a rate of 15 kph while Ludwig moves at 20 kph. Compute how long it would take for them to be 35 km apart.

  A) 15t

  B) 20t

  C) 35

  D) 15t + 20t=35

  E) 1

  F) 1