Question

The cost of manufacturing a cake is directly proportional to the volume of the cake.

The baker makes a 70% profit when he sells a large rectangular cake.
The baker sells a large rectangular cake for £6.80 The baker decides to sell smaller rectangular cakes.
The length, width, and height of the smaller cakes are all half of those of the large rectangular cake.
He sells a pack of 6 of the smaller cakes for £6.50

How much profit does he make on the pack of smaller cakes?

Answer 1

• The baker makes £3.50 profit on smaller cakes

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Given

Large cake:

• Price = £6.80,
• Profit = 70%

Small cake:

• Number = 6,
• Price = £6.50,
• Dimensions = each side is 1/2 of the large cake

Solution

The profit is the difference of the cost and selling price.

Find the cost x of large cake:

• x + 70% = 6.80
• 1.7x = 6.80
• x = 4

Find the volume of the pack of smaller cakes, taking the volume of the large cake as a unit:

• 6*(1/2)³ = 6*1/8 = 3/4

Cost of the pack of smaller cakes is proportional to the volume:

• 4*3/4 = 3

Profit made on smaller cakes:

• 6.50 - 3 = 3.50