KS3 Maths · Year 8 · Chapter 12: Compound units · Lesson 3

Unit costs

Year 8About 75 minutesCalculator allowed48 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/ks3-year-8-unit-costs/

Date

Do Now

Quick questions to start.

A1
Needed today
$6$ apples cost £ $2.40$ . Work out the cost of one apple.
[1 mark]
Answer
A2
Needed today
How many grams are there in $1.25$ kg?
[1 mark]
Answer
A3
Last lesson
A block has a mass of $96$ g and a volume of $40$ cm³. Work out its density.
[1 mark]
Answer
A4
Year 7
Increase £ $40$ by $15%$ .
[1 mark]
Answer

Example, then your turn

Year 8

A unit price is the cost of one unit, such as $1$ g, $100$ g or $1$ litre. The lower the unit price, the better the value. Your teacher works through each example with you. Then try the one beside it.

Example 1

A $400$ g bag of rice costs £ $1.20$ . Work out the cost of $100$ g.

Hint

400

g is

4

lots of

100

B1
A $750$ g box of cereal costs £ $2.85$ . Work out the cost of $100$ g.
[2 marks]
Answer $\dots$ p

Example 2

A $500$ g bag of flour costs $80$ p. How many grams do you get for £ $1$ ?

Hint Work out the grams for

1

p first. £

1

100

B2
A $300$ g jar of honey costs £ $1.20$ . How many grams do you get for £ $1$ ?
[2 marks]
Answer $\dots$ g

Example 3

Rice is sold in a $250$ g bag for £ $1.10$ and in a $400$ g bag for £ $1.68$ . Which bag is better value?

Hint Work out the cost of

1

g for each bag, in pence.

B3
Shampoo is sold in a $300$ ml bottle for £ $2.70$ and in a $450$ ml bottle for £ $3.96$ . Which bottle is better value? Show how you decide.
[3 marks]

Example 4

Potatoes cost £ $3.15$ for a $1.5$ kg bag or $88$ p for a $400$ g bag. Which bag is better value?

Hint Change

1.5

kg into grams first, so both sizes are in the same unit.

B4
Orange juice costs £ $1.44$ for a $1.2$ litre carton or $42$ p for a $330$ ml carton. Which carton is better value? Show how you decide.
[3 marks]

Example 5

$200$ g of cheese costs £ $2.40$ . At the same price per gram, how much does $350$ g cost?

Hint Work out the cost of

50

g, a size that goes into both

200

g and

350

B5
A $150$ ml tube of sun cream costs £ $2.10$ . At the same price per ml, how much does a $225$ ml tube cost?
[2 marks]
Answer£ $\dots$

Practice

Year 8

C1
One can of lemonade costs $75$ p. A pack of $6$ of the same cans costs £ $3.99$ . Which is better value? Give a reason.
[2 marks]
C2
Three people buy potatoes from different shops. The table shows what each paid. Who got the best value? Show how you decide.
[3 marks]

C3
The graph shows the price of grapes. Use the graph to find the cost of grapes in pence per $100$ g, and in £ per kg.
[3 marks]
C4
Coffee is sold in two sizes. The table shows the mass and the price of each. Which size is better value? Show how you decide.
[3 marks]
C5
Tea bags cost £ $2.40$ for a box of $80$ , or £ $6.60$ for a box of $240$ . Jen needs $240$ tea bags. How much does she save by buying one box of $240$ instead of boxes of $80$ ?
[2 marks]
Answer $\dots$ p

Exam-style questions

GCSE Foundation

D1
A $750$ ml bottle of oil costs £ $1.80$ . A $2$ litre bottle of the same oil costs £ $5.00$ . Sam says: "The bigger bottle is always better value."
Show that Sam is wrong for these two bottles.
[3 marks]

D2
A $500$ g pack of mince costs £ $4.40$ . In a special offer, two of these packs cost £ $7.60$ .
(a)
Work out the reduction in the cost of $100$ g of mince when you buy the special offer.
[3 marks]
Answer $\dots$ p
(b)
Write this reduction as a percentage of the usual cost of $100$ g. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots %$
Total for D2: 5 marks
D3
A shop sells nuts in a $250$ g bag for £ $1.75$ and in a $600$ g bag for £ $3.90$ . The shop wants to sell a new $1$ kg bag that is better value than both of these bags. The price is a whole number of pence. What is the most the shop can charge for the $1$ kg bag?
[4 marks]
Answer£ $\dots$
D4
A pack of $6$ pots of yogurt costs £ $2.70$ . Each pot holds $125$ g. A large pot of the same yogurt costs £ $1.98$ . The large pot is better value than the pack. What can you say about the mass of the large pot?
[4 marks]
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A can of juice usually costs $60$ p. Shop A has the offer "buy $3$ , get $1$ free". Shop B has $20%$ off every can. Ali needs $12$ cans. Which shop is cheaper for him, and by how much?
[3 marks]
Hint 1 · What to try
At shop A, how many of the $12$ cans does Ali pay for?
Hint 2 · The first line
At shop A he pays for $9$ cans. At shop B each can costs $80%$ of $60$ p.
Hint 3 · The full method
Shop A: $9 \times 60$ p. Shop B: $12 \times 48$ p.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out a unit price, such as the cost of $100$ g.
I can work out how much I get for £ $1$ .
I can compare sizes to find the better value, changing units first.
I can use a unit price to solve a problem about value.

Answers and mark scheme

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.

Get the answers