P6 Algebra Problem Sums ALB1

ALB 1

Part-Whole Model  |  Finding the Total (One-Step)

When a quantity is unknown, we use a letter (like n) to represent it. A part-whole model helps us see the parts that make up the total, so we can write an algebraic expression for the answer.
✏️  Guided Example
Jane had 5 packets of beads. Each packet contained n beads. Her mother gave her another 20 beads. How many beads did she have in the end?
STEP 1
Understanding the Problem

How many packets of beads were there?

▶ 5

How many beads were there in each packet?

▶ n

How many beads did Jane’s mother give her?

▶ 20

What am I trying to find?

▶ The total number of beads Jane had in the end.

STEP 2
Devising a Plan

▶ Draw a part-whole model.

? n n n n n 20 5 packets of n beads given by mum
STEP 3
Carrying Out the Plan
(5 × n) + 20
= 5n + 20
She had 5n + 20 beads in the end.
STEP 4
Looking Back

Check all the steps and calculations.

(5 × n) + 20
= n + n + n + n + n + 20
= 5n + 20 ✓
💡 Key Idea: When items are in groups of the same unknown, multiply the number of groups by the letter. Then add any extra amount to get the total expression.
ALB 1

Practice – Part-Whole Model (Finding Total)

Score 0 / 8
📝 Answer both parts of each question, then click Lock In Answers to check your score. You can only reveal the worked solution after locking in.
1

Daniel had 20 packs of pens. Each pack contained q pens. He then bought another 35 pens.

(i)  1 mark
How many pens are there in the 20 packs? Give your answer in terms of q.
(ii)  1 mark
How many pens did Daniel have in total in the end? Give your answer in terms of q.
✅ Worked Answer
? 20 × q = 20q 35
(i)  20 packs × q pens = 20q
(ii) 20q + 35
Daniel had 20q + 35 pens in the end.
2

Don, Alice, Gary and Wayne each had $w. Gary’s father gave him another $325.

(i)  1 mark
How much money did the 4 children have at first altogether? Give your answer in terms of w.
(ii)  1 mark
How much money did the 4 children have altogether in the end? Give your answer in terms of w.
✅ Worked Answer
? w w w w $325
(i)  4 children × $w = $4w
(ii) 4w + 325
The four children had $(4w + 325) altogether.
3

Terry had 8 boxes of marbles. Each box contained y marbles. He then bought another 38 green and 29 red marbles.

(i)  1 mark
How many marbles were in the 8 boxes? Give your answer in terms of y.
(ii)  1 mark
How many marbles did Terry have in total in the end? Give your answer in terms of y.
✅ Worked Answer
? 8 × y = 8y 38 + 29 = 67
(i)  8 boxes × y = 8y
(ii) Extra = 38 + 29 = 67
     8y + 67
Terry had 8y + 67 marbles in the end.
4

Janet made 4 jugs of apple juice and 6 jugs of orange juice. Each jug contained p litres. She then made another 3 litres of lemon juice.

(i)  1 mark
How many litres of juice were in the jugs altogether? Give your answer in terms of p.
(ii)  1 mark
How many litres of fruit juice did Janet have altogether in the end? Give your answer in terms of p.
✅ Worked Answer
? (4+6) × p = 10p 3 ℓ
(i)  Total jugs = 4 + 6 = 10
     10 × p = 10p
(ii) 10p + 3
Janet had 10p + 3 litres of fruit juice altogether.
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