## Two different types of cake are on sale at prices of $0.30 and$0.40 each. The cakes that are being sold for $0.30 cost 0.20 to make and the Question Two different types of cake are on sale at prices of$0.30 and $0.40 each. The cakes that are being sold for$0.30 cost 0.20 to make and the ones being sold for $0.40 cost$0.25 to make. No cakes can be kept to be sold the next day, so all of the cakes are being reduced to half price 2 hours before the sale finish. All of the $0.30 cakes sold out before any of the prices were reduced, and all of the$0.40 were eventually sold out, even though only half had been sold when the price was reduced. The overall profit at the end of the day was $30.00, but it could have been$40.00 if all of the cakes had been sold before the prices were reduced. How many of each type of cake were there in the sale?

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3 months 2022-02-19T07:38:02+00:00 1 Answer 0 views 0

There were 250 cakes of selling price $0.30 and 100 cakes of selling price$0.40

Step-by-step explanation:

Assume that the number of cakes that price $0.30 is x and the number of cakes that price$0.40 is y

∵ The cakes that are being sold for $0.30 cost 0.20 to make – The profit = selling price – cost price ∴ The profit of each cake is = 0.30 – 0.20 = 0.10 ∵ The number of that cakes is x The profit of x cakes = 0.10 x All of the cakes are being reduced to half price 2 hours before the sale finish ∵ Half of y cakes had been sold when the price was reduced ∵ The cost of each one is$0.40

– That means the selling price of half y is 0.40 and the selling

price of other half y is ( $$\frac{1}{2}$$ × 0.40 = 0.20)

∴ The selling price of y cakes = $$\frac{1}{2}$$ y × 0.40 + $$\frac{1}{2}$$ y × 0.20

∴ The selling price of y cakes = 0.20 y + 0.10 y

∴ The selling price of y cakes = 0.30 y

∵ The ones of y costs $0.25 to make ∴ The total cost of y cakes = 0.25 y ∴ The profit of y cakes = 0.30 y – 0.25 y The profit of y cakes = 0.05 y ∵ The overall profit at the end of the day was$30.00

– Add the profits of x and y, then equate the sum by 30

0.10 x + 0.05 y = 30 ⇒ (1)

It could have been $40.00 if all of the cakes had been sold before the prices were reduced ∵ The profit of all x = 0.10 x ∵ The profit of all y = (0.40 – 0.25) × y ∴ The profit of all y = 0.15 y – Add 0.10 x and 0.15 y, then equate the sum by 40 0.10 x + 0.15 y = 40 ⇒ (2) Now we have a system of equation to solve it Subtract equation (1) from equation (2) to eliminate x ∵ (0.10 x – 0.10 x) + (0.15 y – 0.05 y) = (40 – 30) ∴ 0.10 y = 10 – Divide both sides by 0.10 y = 100 Substitute the value of y in equation (1) to find x ∵ 0.10 x + 0.05(100) = 30 ∴ 0.10 x + 5 = 30 – Subtract 5 from both sides ∴ 0.10 x = 25 – Divide both sides by 0.10 x = 250 There were 250 cakes of selling price$0.30 and 100 cakes of selling price \$0.40