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Dave buys a goat and sheep for a total price of £120 as is surprised to find that the goat was twice the price of the sheep..

He made twice as much profit on the sheep as he did on the goat having sold both for a combined price of £180.

What is the percentage profit on the sheep?

Sagot :

facundo3141592

Answer:

Let's define:

G = cost of a goat

S = cost of a sheep.

We know that the total cost for a goat and a sheep is £120, then:

S + G = £120

And the cost of the goat is twice the price of the sheep, then:

G = 2*S

To solve this system, we can just replace the second equation into the first one, then we get:

S + (2*S) =  £120

3*S =  £120

S =  £120/3 =  £40

This means that each sheep costs  £40

And the cost of a goat is:

G = 2* £40 =  £80.

Now we know that he sold both of them, where:

s = price of the sheep

g = price of the goat.

We know that he sold both of them for £180, then:

s + g = £180

And the profit of the sheep is twice the profit of the goat, then:

(s - S) = 2*(g - G)

(s -  £40) = 2*(g -  £80)

s  -  £40 = 2*g -  £160

Then we have a system of equations:

s + g = £180

s  -  £40 = 2*g -  £160

To solve this, we first could isolate g in the first equation:

g = £180 - s

Replacing this in the other equation we get:

s - £40 = 2*( £180 - s) -  £160

s - £40 = £360 - 2*s - £160

s - £40 = £200 - 2*s

s + 2*s = £200 - £40 = £160

3*s = £160

s = £160/3 = £53.33

Then the percentage profit for the sheep is:

percentage profit = (s/S)*100% = (£53.33/£40)*100% = 133.3%

Then the percentae profit is 33.3%, which means that the sheep was sold at 133.3% of its original cost, leaving a profit of 33.3% of its original cost.

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