Example 1:
Ali is m years old. Bala is 8 years older than Ali.
(a) What is Bala's age in terms of m?
(b) What is their total age in terms of m?
(c) What is their total age in 10 years' time? Give your answer in terms of m.
Think: Bala is older, so Ali is younger.
Ali is m years old. Bala is 8 years older, so we need to add 8 to m.
Ans(a): Bala is (m + 8) years old
Ali's age → m
Bala's age → m + 8
So, their total age is:
m + (m + 8) = 2m + 8
Ans(b): (2m + 8) years
For part (c), it is useful to use a table:
| Ali | Bala | Total |
Now | m | m + 8 | 2m + 8 |
In 10 years’ time | m + 10 | m + 18 | 2m + 28 |
(m + 10) + (m + 18) = 2m + 28
Ans(c): (2m + 28) years
There are 2 points to take note of here:
1) The terms containing letters such as m and the terms without letters do not mix, but are dealt with separately. Also, each letter such as m should represent only one value.
2) When writing down the answer, we always put the whole expression in brackets. For example, if we write the answer for part (c) as 2m + 28 years, it is considered wrong, because (2m + 28) is considered a single expression and must be enclosed in brackets.
Example 2:
Don is 12 years old. He is w years older than Harry.
(a) How old is Harry?
(b) What is their total age?
(c) What is their total age in 5 years' time?
(Give your answers in term of w.)
Think: Don is older than Harry. So Harry is younger.
Don is 12 years old.
Harry is w years younger than Don.
So, Harry's age → 12 – w
Ans(a): (12 - w) years
Don's age → 12 years
Harry's age → 12 – w
Total age → 12 + 12 – w = 24 – w
Ans(b) (24 – w) years
For part (c), it is useful to use a table:
| Don | Harry | Total |
Now | 12 | 12 – w | 24 – w |
In 5 years’ time | 12 + 5 = 17 | 12 – w + 5 = 17 – w | 34 – w |
17 + (17 – w) = (34 – w)
Ans(c): (34 – w) years
Example 3:
A pencil cost q cents. Suzy bought 8 pencils. How much did she pay for the pencils? Give your answer in terms of q.
8 × q = 8q
Ans: 8q cents
Example 4:
John and Peter were given y sweets to be shared equally. John ate 3 of the sweets. How many sweets did John have left? Give your answer in terms of y.
John took half of the sweets. That means he took y⁄2 sweets.
He ate 3 of the sweets, so he had (y⁄2 – 3) sweets left.
Ans: (y⁄2 – 3) sweets
Example 5:
Tom is 5m years old. His grandfather is 4 times as old as he is.
(a) How old is Tom's grandfather?
(b) What is their total age now?
(c) What is their total age in 10 years' time?
(Give your answers in term of m.)
Think: Don is older than Harry. So Harry is younger.
Tom is 5m years old.
His grandfather is 4 times his age.
So, his grandfather's age → 4 × 5m = 20m
Ans(a): 20m years
For parts (b) and (c), it is useful to use a table:
| Tom | Grandfather | Total |
Now | 5m | 20m | 25m |
In 5 years’ time | 5m + 10 | 20m + 10 | 25m + 20 |
5m + 20m = 25m
Ans(b): 25m years
In 10 years' time,
Tom's age → (5m + 10) years
Grandfather's age → (20m + 10) years
Total age → (5m + 10) + (20m + 10)
= 5m + 10 + 20m + 10
= 25m + 20
Ans(c) (25m + 20) years
Example 6:
Jim, Larry and Ron contributed some money to buy a present. Jim contributed $5m. Larry contributed half as much as Jim. Ron contributed $7 less than Larry. How much did the present cost?
Give your answer in terms of m in the simplest form.
Jim's contribution → $5m
Larry's contribution → 1⁄2 × $5m = $21⁄2m (Note: m is a numerator)
Ron's contribution → $3m – $7 = $(3m – 7)
Total age → $6m + $21⁄2m + $(3m – 7)
= $(6m + 21⁄2m + 3m – 7)
= $(111⁄2m – 7) (Note: m is a numerator)
Ans: $(111⁄2m – 7)
