P6 Algebra Problem Sums ALB2

ALB 2

Part-Whole Model  |  Finding a Part (One-Step)

In ALB 1, the unknown was the size of each group (e.g. n beads per packet).
In ALB 2, the unknown is the number of groups (e.g. m boxes). Each group has a known fixed amount. We still use the part-whole model to find the total.
✏️  Guided Example
Bernice had m boxes of hair clips. Each box contained 4 hair clips. She then bought another 8 hair clips. How many hair clips did she have in the end?
STEP 1
Understanding the Problem

How many boxes of hair clips did Bernice have?

▶ m

How many hair clips were there in each box?

▶ 4

How many hair clips did she buy?

▶ 8

What am I trying to find?

▶ The total number of hair clips Bernice had in the end.

STEP 2
Devising a Plan

▶ Draw a part-whole model.

? 4 4 4 . . . 8 m boxes, 4 clips each bought extra
STEP 3
Carrying Out the Plan
(m × 4) + 8
= 4m + 8
She had 4m + 8 hair clips in the end.
STEP 4
Looking Back

Check all the steps and calculations.

(m × 4) + 8
= 4 × m + 8
= 4m + 8 ✓
💡 Key Idea: When the number of groups is the unknown letter, multiply the letter by the known fixed amount per group, then add any extra to get the total expression.
ALB 2

Practice – Part-Whole Model (Finding a Part)

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers to check your score. Worked solutions are only revealed after locking in.
1

The average height of a group of y children was 135 cm. Jack, who is 120 cm tall, joined the group.

(i)  1 mark
What was the total height of the y children before Jack joined? Give your answer in terms of y.
(ii)  1 mark
What was the new total height of the group after Jack joined? Give your answer in terms of y.
✅ Worked Answer
? y × 135 = 135y 120 cm
(i)  y children × 135 cm = 135y cm
(ii) 135y + 120
New total height = 135y + 120 cm
2

A container had 600 ml of water. Ali then poured k bottles of water into the container. Each bottle contained 250 ml.

(i)  1 mark
How many ml of water did Ali pour in altogether? Give your answer in terms of k.
(ii)  1 mark
How many ml of water were in the container in the end? Give your answer in terms of k.
✅ Worked Answer
? 600 ml k × 250 = 250k
(i)  k bottles × 250 ml = 250k ml
(ii) 600 + 250k
Total water = 250k + 600 ml
3

There are q cars and 35 motorcycles at a car park. Each car has 4 wheels and each motorcycle has 2 wheels.

(i)  1 mark
How many wheels do the q cars have? Give your answer in terms of q.
(ii)  1 mark
How many wheels are there altogether? Give your answer in terms of q.
✅ Worked Answer
? q × 4 = 4q (cars) 35×2 = 70 (bikes)
(i)  q cars × 4 wheels = 4q
(ii) Motorcycles: 35 × 2 = 70
     4q + 70
Total wheels = 4q + 70
4

There are m tables and 30 chairs in a shop. Each table costs $499 and each chair costs $60.

(i)  1 mark
What is the total cost of the m tables? Give your answer in terms of m.
(ii)  1 mark
What is the total cost of all the tables and chairs? Give your answer in terms of m.
✅ Worked Answer
? m × $499 = $499m 30×$60 = $1800
(i)  m tables × $499 = $499m
(ii) Chairs: 30 × $60 = $1800
     $499m + $1800
Total cost = $(499m + 1800)

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