P6 Algebra Problem Sums ALB4

ALB 4

Comparison Model  |  Finding the Difference (One-Step)

In ALB 3, a known amount was given away from an unknown total.
In ALB 4, the number of groups is unknown (the letter), each group has a known fixed amount, and a specific item is removed. We subtract that item’s value from the total to find what remains.
✏️  Guided Example
The average capacity of h pails was 5 ℓ. A pail of capacity 8 ℓ was then removed from the group. What was the new total capacity of the remaining pails?
STEP 1
Understanding the Problem

How many pails were there in the original group?

▶ h

What was the average capacity of the pails?

▶ 5 ℓ

What was the capacity of the pail that was removed?

▶ 8 ℓ

What am I trying to find?

▶ The new total capacity of the remaining pails.

STEP 2
Devising a Plan

▶ Draw a comparison model.

h pails 5 ℓ 5 ℓ . . . left, ? 8 ℓ removed remaining pails removed pail
STEP 3
Carrying Out the Plan
(h × 5) − 8
= 5h − 8
The new total capacity was 5h − 8 ℓ.
STEP 4
Looking Back

Check all the steps and calculations.

(h × 5) − 8
= 5 × h − 8
= h + h + h + h + h − 8
= 5h − 8 ✓
💡 Key Idea: Find the total of all groups first (letter × fixed amount), then subtract the specific item removed. The result is the new total of what remains.
ALB 4

Practice – Comparison Model (Finding the Difference)

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers. Find the total first, then subtract what was removed.
1

Willy bought k boxes of pens. Each box contained 28 pens. He then gave 50 pens to his brother.

(i)  1 mark
How many pens did Willy have in total at first? Give your answer in terms of k.
(ii)  1 mark
How many pens did Willy have left? Give your answer in terms of k.
✅ Worked Answer
(i)  k boxes × 28 pens = 28k
(ii) 28k − 50
Willy had 28k − 50 pens left.
2

John saved an average of $5 a day for m days. He then bought a present for $55.

(i)  1 mark
How much did John save altogether? Give your answer in terms of m.
(ii)  1 mark
How much money did John have left? Give your answer in terms of m.
✅ Worked Answer
(i)  m days × $5 = $5m
(ii) $5m − $55
John had $(5m − 55) left.
3

The average cost of w cabinets was $125. A cabinet which cost $132 was removed from the group.

(i)  1 mark
What was the total cost of all w cabinets? Give your answer in terms of w.
(ii)  1 mark
What was the new total cost of the remaining cabinets? Give your answer in terms of w.
✅ Worked Answer
(i)  w cabinets × $125 = $125w
(ii) $125w − $132
New total cost = $(125w − 132)
4

The average mass of p sacks of rice was 22 kg. 3 sacks of rice with an average mass of 20 kg were then removed.

(i)  1 mark
What was the total mass of all p sacks? Give your answer in terms of p.
(ii)  1 mark
What was the new total mass of the remaining sacks? Give your answer in terms of p.
✅ Worked Answer
(i)  p sacks × 22 kg = 22p kg
(ii) Removed = 3 sacks × 20 kg = 60 kg
     22p − 60
New total mass = 22p − 60 kg

Scroll to Top