Question

Rana sells 192 cakes in the ratio small: medium: large = 7 : 6 : 11.

The profit for one medium cake is twice the profit for one small cake.
The profit for one large cake is three times the profit for one small cake.
Her total profit is £532.48
Work out the profit for one small cake

Answer 1

S = £1.28

Explanation:

Let the small, medium and large cakes be S, M and L respectively.

Given the following data;

Total profits = £532.48

Total number of cake = 192 cakes

Ratio of S:M:L = 7:6:11

Sum of ratio = 7+6+11 = 24

To find number of each cakes, we would divide the total number of cakes by the sum of ratio;

Number of each cakes = 192/24

Number of each cakes = 8

Next, we determine the exact number of each type of cakes.

Small = 7*8 = 56 cakes.

Medium = 6*8 = 48 cakes.

Large = 11*8 = 88 cakes.

For the profits;

Translating the word problem into an algebraic expression, we have;

M = 2S

L = 3S

56S + 48*(2S) + 88*(3S) = £532.48

56S + 96S + 264S = 532.48

416S = 532.48

S = 532.48/416

S = £1.28

Therefore, the profit for one small cake is £1.28