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The arithmetic mean of three numbers is 147. If the mean of the first two numbers is 141, what is the third number?

A. 141
B. 147
C. 150
D. 156

Answer :

Final answer:

After calculating using the given means of the first two numbers and all three numbers, the third number is determined to be 159, which is not listed among the provided options.

Explanation:

The arithmetic mean of three numbers is 147. To find the mean, we add together the individual measurements and divide by the number of measurements. If the mean of the first two numbers is 141, we can set up the following equation to find the mean of all three numbers: Let x, y be the first two numbers, and z be the third number.

According to the question:

(x + y)/2 = 141

(x + y + z)/3 = 147

From the first equation we can derive that x + y = 141 * 2 = 282. Plugging this into the second equation:

(282 + z)/3 = 147

Multiplying both sides by 3 gives us:

282 + z = 441

To find the third number, z, we subtract the sum of the first two numbers from the total sum:

z = 441 - 282

z = 159

Therefore, the third number is 159, which is not one of the provided options. There may be a mistake in the options or in the question.

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