SOLUTION: The profit earnings for XYZ co. are reported quarterly. The earnings as a % of the yearly earnings for 2007 are 1st quarter 25%, 2nd quarter 15%, 3rd quarter 38%, 4th quarter 22%.

Question 304923: The profit earnings for XYZ co. are reported quarterly. The earnings as a % of the yearly earnings for 2007 are 1st quarter 25%, 2nd quarter 15%, 3rd quarter
38%, 4th quarter 22%. If the earnings in the 1st quarter were $54,000, what were the earnings for the third quarter? Please show step by step work and include units in the solution.
Thank you
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The quarterly profit earning for XYZ corporation are:

First quarter equals 25%
Second quarter equals 15%
Third quarter equals 38%
Fourth quarter equals 22%

These earning are expressed as a percent of the yearly earnings for 2007.

If the first quarter earnings were $54,000, this means that the yearly earnings must have been $54,000 / .25 = $216,000.

25% of $216,000 equals $54,000

Now that you have the yearly earnings, you can determine the earnings for each quarter.

They would be:

First quarter equals 25% of $216,000 = $54,000
Second quarter equals 15% of $216,000 = $32,400
Third quarter equals 38% of $216,000 = $82,080
Fourth quarter equals 22% of $216,000 = $47,520

Sum up the quarterly earnings to get $216,000

The question is what were the earnings in the third quarter.

the answer is $82,080.

You could have solved it directly without actually determining the yearly eaarnings as follows:

Let Y equal the yearly earnings.

.25 * Y = $54,000 which means that Y = $54,000 / .25

The third quarter earnings are equal to .38 * Y.

Since you know that Y = $54,000 / .25, then the third quarter earnings are equal to:

.38 * ($54,000/.25) which becomes (.38/.25) * ($54,000) which becomes 1.52 * $54,000 which becomes $82,080.

Third quarter earnings are $82,080.

You get the same answer either way.

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