P6 Algebra Problem Sums ALB7

ALB 7

Part-Whole Model  |  Subtract then Divide (One-Step)

In ALB 5 & 6, we added parts together then divided.
In ALB 7, we first subtract a known amount from the total, then divide what remains equally into groups. The answer is a fraction expression: (total − given away) ÷ containers.
✏️  Guided Example
Mrs Sim bought 7 boxes of pencils. Each box contained y pencils. She gave her pupils 56 pencils. She then kept all the remaining pencils equally in 8 containers. How many pencils were there in each container?
STEP 1
Understanding the Problem

How many boxes of pencils did Mrs Sim buy?

▶ 7

How many pencils did each box contain?

▶ y

How many pencils did she give her pupils?

▶ 56

How many containers did she keep the remaining pencils equally in?

▶ 8

What am I trying to find?

▶ The number of pencils in each container.

STEP 2
Devising a Plan

▶ Draw a comparison model — find the total, subtract what was given away, then divide what remains.

7 boxes of y pencils = 7y Total: y y y y . . . remaining, ? 56 given to pupils 7y − 56 remaining ÷ 8: ? ? ? ? ? ? ? ? 8 equal containers — each has (7y − 56) / 8 pencils
STEP 3
Carrying Out the Plan
(7 × y − 56) ÷ 8
= (7y − 56) ÷ 8
= (7y − 56) / 8
There were (7y − 56) / 8 pencils in each container.
STEP 4
Looking Back

Check all the steps and calculations.

Total pencils = 7 × y = 7y
After giving away 56: 7y − 56
Each container = (7y − 56) ÷ 8 ✓
💡 Key Idea: Find the total first, then subtract what was given away. Finally divide what remains equally: (total − given away) ÷ number of containers.
ALB 7

Practice – Subtract then Divide

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers. Write fraction answers as (expression) / number, e.g. (7y − 56) / 8.
1

A group of 6 children had p marbles on average. Gerald who had 45 marbles left the group. What was the average number of marbles the remaining children had?

💡 Total = 6p. Remove Gerald’s 45. Divide by 5 remaining children.
(i)  1 mark
What was the total number of marbles the remaining 5 children had? Give your answer in terms of p.
(ii)  1 mark
What was the average number of marbles the remaining 5 children had? Give your answer in terms of p.
✅ Worked Answer
Total: 6 × p = 6p remaining, ? 45 Gerald left 6p − 45 remaining ÷ 5: ? ? ? ? ? 5 remaining children — average = (6p − 45) / 5
(i)  Total = 6 × p = 6p
     After Gerald left: 6p − 45
(ii) Children left = 6 − 1 = 5
     Average = (6p − 45) ÷ 5
Average = (6p − 45) / 5
2

Cheryl bought 7 bottles of milk. Each bottle contained w ℓ of milk. She drank 2 ℓ of milk in the first three days and poured the rest equally into 4 jugs. How many litres of milk did each jug contain?

💡 Total = 7w. Subtract 2 ℓ drunk. Divide by 4 jugs.
(i)  1 mark
How many litres of milk were left after Cheryl drank 2 ℓ? Give your answer in terms of w.
(ii)  1 mark
How many litres of milk did each jug contain? Give your answer in terms of w.
✅ Worked Answer
Total: 7 × w = 7w remaining, ? 2 ℓ drunk 7w − 2 remaining ÷ 4: ? ? ? ? 4 jugs — each has (7w − 2) / 4 ℓ
(i)  Total = 7 × w = 7w
     After drinking: 7w − 2
(ii) (7w − 2) ÷ 4
Each jug had (7w − 2) / 4 ℓ.
3

Jennifer bought 10 boxes of marbles. Each box contained k marbles. She gave 224 marbles to her brother and kept all the rest equally in 7 jars. How many marbles were there in each jar?

💡 Total = 10k. Subtract 224 given away. Divide by 7 jars.
(i)  1 mark
How many marbles did Jennifer have after giving some to her brother? Give your answer in terms of k.
(ii)  1 mark
How many marbles were there in each jar? Give your answer in terms of k.
✅ Worked Answer
Total: 10 × k = 10k remaining, ? 224 given 10k − 224 remaining ÷ 7: ? ? ? ? ? ? ? 7 jars — each has (10k − 224) / 7 marbles
(i)  Total = 10 × k = 10k
     After giving: 10k − 224
(ii) (10k − 224) ÷ 7
Each jar had (10k − 224) / 7 marbles.
4

The average height of a group of 30 pupils was h cm. 7 pupils of average height 138 cm left the group. What was the average height of the remaining pupils?

💡 Total = 30h. Subtract 7 pupils’ total (7 × 138 = 966). Divide by 23 remaining pupils.
(i)  1 mark
What was the total height of the remaining 23 pupils? Give your answer in terms of h.
(ii)  1 mark
What was the average height of the remaining 23 pupils? Give your answer in terms of h.
✅ Worked Answer
Total: 30 × h = 30h 23 pupils remaining, ? 7×138=966 left 30h − 966 remaining ÷23: 23 remaining pupils — average = (30h − 966) / 23
(i)  Total = 30 × h = 30h
     7 pupils left: 7 × 138 = 966
     Remaining total = 30h − 966
(ii) Pupils left = 30 − 7 = 23
     Average = (30h − 966) ÷ 23
Average height = (30h − 966) / 23 cm

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