Exercise 3 – Forming Algebraic Expressions
1.
A number is represented by 𝑥. 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 𝑏 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 𝑛.
a) What are the 7 numbers in terms of 𝑛?
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 𝑟 balls, in terms of 𝑟, how
many balls did:
a) Andy collect?
b) Maria collect?
c) The total number of balls collected?
5.
6.
7.
I think of a number, multiply it by 5, subtract
2, subtract the original number, and then
halve it. If the starting number was 𝑥, give an
expression for the final answer, as simply as
possibly.
In a list of seven consecutive numbers a
quarter of the smallest number is five less
than a third of the largest number. If 𝑥 is the
smallest number, find expressions for:
a) “a quarter of the smallest number”
b) “five less than a third of the largest
number”
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 𝑛 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 𝑎 and Dally’s 𝑏.
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 𝑎 and one in
terms of 𝑏.
9.
A woman had 9 children at regular intervals of
15 months. The oldest is now six times as old
as the youngest.
a) Let 𝑎 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).
10. 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 𝑡.
a) How much money (in terms of 𝑡) 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”.
11. [JMC 2014 Q20] Box P has 𝑝 chocolates and
box Q has 𝑞 chocolates, where 𝑝 and 𝑞 are
both odd and 𝑝 > 𝑞. 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
D
𝑞−𝑝+2
2
𝑝−𝑞−2
2
B
E
𝑝−𝑞+2
2
𝑞+𝑝+2
C
𝑞+𝑝−2
2
2
12. [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.