problems on average allegation and mixtures

[zeeshan]

guys please help me solving these problems

 

1) a merchant paid $300 for a shipment of x identical calculators .The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average cost of the x calculators .If the total revenue from the sale of the calculators was $120 more than the cost of the shipment,how many calculators were in shipment ?

 

 

A) 24 B) 25 C)26 D)28 E)30

 

 

2)A corporation with 5,000,000 shares of publicily listed stock reported total earnings of $7.20 per share for the first 9 months of operation .During the final quarter the number of publicly listed shares was increased to 10,000,000 shares,and fourth quarter earnings were reported as $1.25 per share .what are the average annual earnings per share based on the number of shares at the end of the year ?

 

 

A)$1.83 B)$2.43 C)$4.85 D)$8.45

 

3)How many litres of pure alcohol must be added to a 80 litre solution that is 25 percent pure alochol in order to produce the solution contains 40 percent or 60 percent alcohol.

 

 

A)15 litres B)20litres C)40litres D)65litres E)70litres

[twohundredping]

You probably want to post these questions in the forum section for the math section of the general GRE. This forum is located here: GRE Math

 

I'll answer 1 and 3 since I don't really understand 2.

 

1)

Let x be the amount of calculators in the shipment.

Since $300 on x calculators then the average cost of a calculator must be 300/x.

He sells x-2 or these calculators for $5 more than their average cost, i.e. 300/x +5

 

His revenue (which doesn't include the cost of him purchasing the items) is $420

For this problem we can simply express his revenue as the product of the items sold and the price per item.

Revenue = (number of items sold) * (price per item)

420 = (x - 2) * (300/x + 5) (now solve for x)

420x = (x - 2) * (300 + 5x)

420x = 300x + 5x^2 - 600 - 10x

0 = 5x^2 - 130x - 600

0 = x^2 - 26x - 120

0 = (x - 30) (x + 4)

x =-4 or x =30

Clearly we must take the positive answer so x = 30. E.

 

3)

80 liter solution is 25 percent alcohol. Note that 25% = 1/4. So 1/4 of the solution is alcohold and 1 - 1/4 = 3/4 of the solution is water.

Originally we have 80 * 1/4 = 20 liters alcohol and 80 * 3/4 = 60 liters water.

 

Let us first consider making a 40 percent alcohol solution.

We can simply figure out how much alcohol needs to be combined with 60 liters water to yield 40 percent alcohol. And we can express 40% as 2/5

Let x represent the amount of alcohol.

(amount of alcohol) / (amount of solution) = percent alcohol

x / (x + 60) = 2/5

5x = 2 * (x + 60)

5x = 2x + 120

3x = 120

x = 40

 

So if we combine 40 liters alcohol with 60 liters water we get a solution that is 40% alcohol. Since we originally had 20 liters alcohol, 40 - 20 = 20 liters alcohol must be added. So B is an answer.

 

 

Now lets consider making a 60 percent alcohol solution.

Again, we can simply figure out how much alcohol needs to be combined with 60 liters water to yield 60 percent alcohol. And we can express 60% as 3/5

Let x represent the amount of alcohol.

(amount of alcohol) / (amount of solution) = percent alcohol

x / (x + 60) = 3/5

5x = 3 * (x + 60)

5x = 3x + 180

2x = 180

x = 90

 

So if we combine 90 liters alcohol with 60 liters water we get a solution that is 60% alcohol. Since we originally had 20 liters alcohol, 90 - 20 = 70 liters alcohol must be added. So E is an answer.

 

B and E are the two answers.

[mxplusb]

If I understand the second problem correctly, the answer is the earnings per share for the fourth quarter, plus the earnings per share for the first nine months if there had been 10,000,000 shares. There weren't, there were 5,000,000 shares, which each earned $7.20 per share. If earnings in the first three-quarters of the year was $7.2p per share, total earnings must have been $7.20*5 = $36 million. If there had been 10 million shares, (divide by 10 million) it would have been $3.60 per share. Adding $3.60 to $1.25 you get © $4.80.

 

I may be misinterpreting.

[thepillow]

If I understand the second problem correctly, the answer is the earnings per share for the fourth quarter, plus the earnings per share for the first nine months if there had been 10,000,000 shares. There weren't, there were 5,000,000 shares, which each earned $7.20 per share. If earnings in the first three-quarters of the year was $7.2p per share, total earnings must have been $7.20*5 = $36 million. If there had been 10 million shares, (divide by 10 million) it would have been $3.60 per share. Adding $3.60 to $1.25 you get © $4.80.

 

I may be misinterpreting.

 

Hey mxplusb,

 

I have no idea if I'm interpreting it any more correctly than you are, but here's one option:

 

First 3 quarters: 5million * 7.2 = 36million in earnings

 

Final quarter: 10million * 1.25 = 12.5million in earnings

 

Total yearly earnings: 36 + 12.5 = 48.5million

 

Then, if they want to know the average earnings per share assuming the final number of shares, we can divide by 10million giving us $4.85/share.

 

 

What do you think?