Exercise 3 – Forming Algebraic Expressions

  1. A number is represented by . How would we represent:
    a) 2 more than the number.
    b) 5 times the number.
    c) 3 less than than twice the number.
    d) Twice as much as 3 less than the number.
    e) A quarter of the number.
  2. The cost of a badger is pence. A racoon is 5 pence more expensive than a badger and a beaver three times as expensive as a badger.
    a) What is the cost of a racoon?
    b) What is the cost of a beaver?
    c) What is the total cost of a racoon and 8 beavers?
  3. You have 7 consecutive numbers, with the smallest number a) What are the 7 numbers in terms of ?
    b) Hence what is the sum of all the numbers?
  4. After tennis training, Andy collects twice as many balls as Roger and five more than Maria. If Roger collected balls, in terms of , how many balls did:
    a) Andy collect?
    b) Maria collect?
    c) The total number of balls collected?
  5. I think of a number, multiply it by 5, subtract 2, subtract the original number, and then halve it. If the starting number was , give an expression for the final answer, as simply as possibly.
  6. In a list of seven consecutive numbers a quarter of the smallest number is five less than a third of the largest number. If is the smallest number, find expressions for:
    a) “a quarter of the smallest number”
    b) “five less than a third of the largest number”
  7. Pippa thinks of a number. She adds 1 to it to get a second number. She then adds 2 to the second number to get a third number, adds 3 to the third to get a fourth, and finally adds 4 to the fourth to get a fifth number.
    If is the number she started with, what is the sum of her numbers?
  8. Dilly is 7 years younger than Dally. In 4 years time she will be half Dally’s age.

Let Dilly’s age be and Dally’s .

a)Use the first sentence to write a formula for Dilly’s age in terms of Dally’s.

b)Use the second sentence to write two different expressions for Dilly’s age in 4 years time, one in terms of and one in terms of .

  1. A woman had 9 children at regular intervals of 15 months. The oldest is now six times as old as the youngest.

a)Let be the age of the youngest child (in years). What is the age of the oldest child (be careful!)

b)Hence use the information to form an equation relating the ages of the oldest and youngest child (you need not solve it).

  1. Three brothers and a sister shared a sum of money equally among themselves. If the brothers alone had shared the money, then they would have increased the amount they each received by £20. Suppose the total amount of money is .

a)How much money (in terms of ) do the brothers each get if they share just between them?

b)What expression would represent “an increase of £20 from the previous lower amount they would have got”.

  1. [JMC 2014 Q20] Box P has chocolates and box Q has chocolates, where and are both odd and . What is the smallest number of chocolates which would have to be moved from P to box Q so that box Q has more chocolates than box P?
    A B C

D E

  1. [JMO 2007 B1] Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.