P6 Algebra Problem Sums ALB3

ALB 3

Comparison Model  |  Finding What’s Left (One-Step)

In ALB 1 & 2, we added parts to find a total.
In ALB 3, we subtract a known amount from the total to find what remains. We use a comparison model to show what was given away and what was left.
✏️  Guided Example
Alice bought 5 packets of stickers. Each packet contained n stickers. She then gave 20 stickers to her brother. How many stickers did she have left?
STEP 1
Understanding the Problem

How many packets of stickers did Alice buy?

▶ 5

How many stickers did each packet contain?

▶ n

How many stickers did she give to her brother?

▶ 20

What am I trying to find?

▶ The total number of stickers Alice had left.

STEP 2
Devising a Plan

▶ Draw a comparison model.

Total: n n n n n Parts: left, ? 20 gave to brother
STEP 3
Carrying Out the Plan
(5 × n) − 20
= 5n − 20
She had 5n − 20 stickers left.
STEP 4
Looking Back

Check all the steps and calculations.

(5 × n) − 20
= n + n + n + n + n − 20
= 5n − 20 ✓
💡 Key Idea: When a known amount is removed from the total, write the total expression first, then subtract the known amount. Total − Given Away = Left.
ALB 3

Practice – Comparison Model (Finding What’s Left)

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers. Remember: Total − Given Away = Left.
1

Kelly earned $m a day. She worked 5 days in a certain week and spent $60 altogether that week.

(i)  1 mark
How much did Kelly earn in 5 days? Give your answer in terms of m.
(ii)  1 mark
How much money did Kelly have left? Give your answer in terms of m.
✅ Worked Answer
5 × m = 5m (total earned) left, ? $60 spent
(i)  5 days × $m = $5m
(ii) $5m − $60 = $(5m − 60)
Kelly had $(5m − 60) left.
2

The average mass of rice in 22 bags was p kg. A bag containing 3 kg of rice was removed.

(i)  1 mark
What was the total mass of rice in all 22 bags? Give your answer in terms of p.
(ii)  1 mark
What was the total mass of rice in the remaining bags? Give your answer in terms of p.
✅ Worked Answer
22 × p = 22p (total mass) remaining, ? 3 kg
(i)  22 bags × p kg = 22p kg
(ii) 22p − 3
Remaining mass = 22p − 3 kg
3

Pauline, Jacky, Thomas and Cheryl each had $y. Pauline spent $58 on a purse and Thomas spent $88 on sports shoes.

(i)  1 mark
How much did the 4 children have altogether at first? Give your answer in terms of y.
(ii)  1 mark
How much money did the 4 children have altogether in the end? Give your answer in terms of y.
✅ Worked Answer
4 × y = 4y (total at first) left, ? $58 + $88
(i)  4 children × $y = $4y
(ii) Total spent = $58 + $88 = $146
     4y − 146
They had $(4y − 146) altogether in the end.
4

Lucy bought 8 bottles of milk. Each bottle contained k ml of milk. She then poured 3 cups of milk for her children. Each cup contained 150 ml.

(i)  1 mark
How much milk did Lucy have in the 8 bottles? Give your answer in terms of k.
(ii)  1 mark
How many ml of milk did Lucy have left? Give your answer in terms of k.
✅ Worked Answer
8 × k = 8k ml (total milk) left, ? 3×150 ml
(i)  8 bottles × k ml = 8k ml
(ii) Poured out = 3 × 150 = 450 ml
     8k − 450
Lucy had 8k − 450 ml left.

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