P6 Algebra Problem Sums ALB8

ALB 8

Part-Whole Model  |  Unknown Groups → Subtract → Divide

In ALB 7, the unknown was the size per group (e.g. y per box).
In ALB 8, the unknown is the number of groups (e.g. m packets), each with a known fixed amount. We still subtract then divide.
ALB 7
Unknown = size per group (e.g. y per box)
Number of boxes is known
ALB 8
Unknown = number of groups (e.g. m packets)
Each packet has a known fixed amount
✏️  Guided Example
Howard bought m packets of pens. Each packet contained 7 pens. He then gave 10 pens to his brother. He kept the rest of the pens equally in 5 pencil holders. How many pens did each pencil holder contain?
STEP 1
Understanding the Problem

How many packets of pens did Howard buy?

▶ m

How many pens did each packet contain?

▶ 7

How many pens did he give his brother?

▶ 10

How many pencil holders did he keep the remaining pens equally in?

▶ 5

What am I trying to find?

▶ The number of pens each pencil holder contained.

STEP 2
Devising a Plan

▶ Draw a comparison model.

m packets Total: 7 7 7 7 . . . remaining, ? 10 given to brother 7m − 10 remaining ÷ 5: ? ? ? ? ? 5 pencil holders — each has (7m − 10) / 5 pens
STEP 3
Carrying Out the Plan
(m × 7 − 10) ÷ 5
= (7m − 10) ÷ 5
= (7m − 10) / 5
Each pencil holder contained (7m − 10) / 5 pens.
STEP 4
Looking Back
Total pens = m × 7 = 7m
After giving away 10: 7m − 10
Each holder = (7m − 10) ÷ 5 ✓
💡 Key Idea: When the number of groups is unknown, multiply letter × fixed amount per group to get the total. Then subtract what was given away, and divide what remains equally.
ALB 8

Practice – Unknown Groups → Subtract → Divide

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

Leonard had k boxes of stamps. Each box contained 135 stamps. He then gave 528 stamps to his cousin. He put all the remaining stamps equally into 12 albums. How many stamps did each album contain?

💡 Total = 135k. Subtract 528. Divide by 12 albums.
(i)  1 mark
How many stamps did Leonard have after giving some to his cousin? Give your answer in terms of k.
(ii)  1 mark
How many stamps did each album contain? Give your answer in terms of k.
✅ Worked Answer
k boxes (135 each) Total: k × 135 = 135k remaining, ? 528 given 135k − 528 remaining ÷12: 12 albums — each has (135k − 528) / 12 stamps
(i)  Total = k × 135 = 135k
     After giving: 135k − 528
(ii) (135k − 528) ÷ 12
Each album had (135k − 528) / 12 stamps.
2

Thomas bought y boxes of strawberries. Each box contained 15 strawberries. He then gave 48 strawberries to his siblings. He kept all the remaining strawberries equally into containers of 8. How many containers did he use?

💡 Total = 15y. Subtract 48. Divide by 8 per container to find number of containers.
(i)  1 mark
How many strawberries did Thomas have left after giving some away? Give your answer in terms of y.
(ii)  1 mark
How many containers did he use? Give your answer in terms of y.
✅ Worked Answer
y boxes (15 each) Total: y × 15 = 15y remaining, ? 48 given 15y − 48 remaining ÷ 8: ? ? ? ? ? ? ? ? 8 containers — each has (15y − 48) / 8 strawberries
(i)  Total = y × 15 = 15y
     After giving: 15y − 48
(ii) (15y − 48) ÷ 8
He used (15y − 48) / 8 containers.
3

There were p small baskets of soccer balls. Each small basket contained 32 soccer balls. 16 soccer balls were sold and all the remaining soccer balls were kept equally into 8 big baskets. How many soccer balls did each big basket contain?

💡 Total = 32p. Subtract 16 sold. Divide by 8 big baskets.
(i)  1 mark
How many soccer balls were left after 16 were sold? Give your answer in terms of p.
(ii)  1 mark
How many soccer balls did each big basket contain? Give your answer in terms of p.
✅ Worked Answer
p baskets (32 each) Total: p × 32 = 32p remaining, ? 16 sold 32p − 16 remaining ÷ 8: ? ? ? ? ? ? ? ? 8 big baskets — each has (32p − 16) / 8 soccer balls
(i)  Total = p × 32 = 32p
     After selling: 32p − 16
(ii) (32p − 16) ÷ 8
Each big basket had (32p − 16) / 8 soccer balls.
4

Tommy bought r bags of marbles. Each bag contained 28 white marbles and 45 black marbles. He sold 225 marbles and kept all the remaining marbles equally in boxes of 15. How many boxes did he use?

💡 Each bag = 28 + 45 = 73 marbles. Total = 73r. Subtract 225. Divide by 15.
(i)  1 mark
How many marbles did Tommy have after selling 225? Give your answer in terms of r.
(ii)  1 mark
How many boxes of 15 did Tommy use? Give your answer in terms of r.
✅ Worked Answer
r bags (28+45=73 each) Total: r × 73 = 73r remaining, ? 225 sold 73r − 225 remaining ÷15: 15 boxes — each has (73r − 225) / 15 marbles
(i)  Each bag = 28 + 45 = 73 marbles
     Total = r × 73 = 73r
     After selling: 73r − 225
(ii) (73r − 225) ÷ 15
Tommy used (73r − 225) / 15 boxes.
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