Question

Gina sells 216 cakes in the ratio small :medium:large 5:7:12. 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 id £648.45. Work out the profit for one small cake.

Answer 1

Answer:

The profit for one small cake is £1.31.

Step-by-step explanation:

It is given that that Gina sells 216 cakes in the ratio small:medium:large 5:7:12.

$5+7+12=24$

Number of small cakes = $216\times \frac{5}{24}=45$

Number of medium cakes = $216\times \frac{7}{24}=63$

Number of large cakes = $216\times \frac{12}{24}=108$

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.

Let the profit for one small cake be x. So the profit for one medium and large cake are 2x and 3x respectively.

Her total profit id £648.45.

$45\times x+63\times 2x+108\times 3x=648.45$

$45x+126x+324x=648.45$

$496x=648.45$

Divide both sides 496.

$\frac{496x}{496}=\frac{648.45}{496}$

$x=1.30735887097$

$x\approx 1.31$

Therefore the profit for one small cake is £1.31.

Answer 2

To answer this question you need to first set up the small, medium, large number of cakes as a ratio with a total. From here you will create a new ratio of the correct number of small medium and large Cakes sold using the total 216. The factor would be to multiply by nine. -Step 1 in picture. After this you would read what the relationship is between a medium and a small and the large and the small profits are - Step 2 in picture. After this you would represents the total profit based on the number of small medium and large cakes that were sold. Making this equal to L648.45. To find the profit for one small, you would then divide 648.45 by the 495 you got when you simplify the expression. The answer is L1.31.