P6 Algebra Problem Sums ALB6

ALB 6

Part-Whole Model  |  Unknown Groups + Division (One-Step)

ALB 6 combines two ideas: the number of groups is unknown (the letter), each group has a known fixed amount, and after combining everything, we divide equally into a fixed number of containers.
ALB 5
Unknown = size per group (e.g. n cookies per box)
Number of boxes is known
ALB 6
Unknown = number of groups (e.g. x packets)
Each packet has a known fixed amount
✏️  Guided Example
Janice bought x packets of 35 pink hair clips and a box of 63 green hair clips. She repacked them all equally into 9 boxes. How many hair clips did each box contain?
STEP 1
Understanding the Problem

How many packets of pink hair clips did Janice buy?

▶ x

How many pink hair clips were there in each packet?

▶ 35

How many green hair clips did she buy?

▶ 63

How many boxes did she repack all the hair clips equally into?

▶ 9

What am I trying to find?

▶ The number of hair clips each box contained.

STEP 2
Devising a Plan

▶ Draw a comparison model — find the total, then divide into 9 equal boxes.

x packets 35 35 . . . 63 Total = 35x + 63 ÷ 9: ? ? ? ? ? ? ? ? ? 9 equal boxes — each box contains ?
STEP 3
Carrying Out the Plan
(x × 35 + 63) ÷ 9
= (35x + 63) ÷ 9
= (35x + 63) / 9
Each box contained (35x + 63) / 9 hair clips.
STEP 4
Looking Back

Check all the steps and calculations.

Total hair clips = x × 35 + 63 = 35x + 63
Each box = (35x + 63) ÷ 9
Check: (35x + 63) / 9 × 9 = 35x + 63 ✓
💡 Key Idea: When the number of groups is the unknown letter and each group has a fixed amount, multiply letter × fixed amount to get that part’s total. Add any extra, then divide by the number of equal containers.
ALB 6

Practice – Unknown Groups + Division

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers. Write fraction answers as (expression) / number, e.g. (65w + 120) / 8.
1

Leon had w packets of 65 local stamps each. He also had 120 foreign stamps. He put all of them equally into 8 albums.

💡 Total = 65w + 120. Divide equally into 8 albums.
(i)  1 mark
How many stamps did Leon have altogether? Give your answer in terms of w.
(ii)  1 mark
How many stamps did each album contain? Give your answer in terms of w.
✅ Worked Answer
w packets 65 65 . . . 120 Total = 65w + 120 ÷ 8: ? ? ? ? ? ? ? ? 8 albums — each has (65w + 120) / 8 stamps
(i)  w × 65 + 120 = 65w + 120
(ii) (65w + 120) ÷ 8
Each album had (65w + 120) / 8 stamps.
2

Albert had m boxes of coins. Each box contained 215 coins. His mother gave him another 625 coins. He then put all of them equally into 25 containers.

💡 Total = 215m + 625. Divide by 25.
(i)  1 mark
How many coins did Albert have altogether? Give your answer in terms of m.
(ii)  1 mark
How many coins were there in each container? Give your answer in terms of m.
✅ Worked Answer
m boxes 215 215 . . . 625 Total = 215m + 625 ÷25: 25 containers — each has (215m + 625) / 25 coins
(i)  m × 215 + 625 = 215m + 625
(ii) (215m + 625) ÷ 25
Each container had (215m + 625) / 25 coins.
3

Elaine baked n trays of 20 matcha cookies each. She also baked 49 strawberry cookies. She then put all of them equally into 7 jars.

💡 Total = 20n + 49. Divide by 7.
(i)  1 mark
How many cookies did Elaine bake altogether? Give your answer in terms of n.
(ii)  1 mark
How many cookies were there in each jar? Give your answer in terms of n.
✅ Worked Answer
n trays 20 20 . . . 49 Total = 20n + 49 ÷ 7: ? ? ? ? ? ? ? 7 jars — each has (20n + 49) / 7 cookies
(i)  n × 20 + 49 = 20n + 49
(ii) (20n + 49) ÷ 7
Each jar had (20n + 49) / 7 cookies.
4

Erica bought 6 bags of 33 yellow beads each and y bags of 25 blue beads each. She put all of them equally into 9 boxes.

💡 Yellow = 6 × 33 = 198. Blue = 25y. Total = 198 + 25y. Divide by 9.
(i)  1 mark
How many beads did Erica have altogether? Give your answer in terms of y.
(ii)  1 mark
How many beads were there in each box? Give your answer in terms of y.
✅ Worked Answer
y bags (blue, 25 each) 6×33=198 25 25 . . . Total = 25y + 198 ÷ 9: ? ? ? ? ? ? ? ? ? 9 equal boxes — each has (25y + 198) / 9 beads
(i)  Yellow = 6 × 33 = 198
     Blue = y × 25 = 25y
     Total = 25y + 198
(ii) (25y + 198) ÷ 9
Each box had (25y + 198) / 9 beads.
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