The mean of four numbers is 70. When a fifth number is included, the mean of the five numbers is 80. What is the fifth number?

Explanation:

S = sum of the first four values

S/4 = 70 since we divide the sum by 4 to get the mean of the first four values

S = 280 is the result after multiplying both sides by 4

Let x be the fifth unknown value. Adding it onto S leads to S+x = 280+x. This represents the sum of all five values.

Dividing that sum 280+x over 5 leads to the new mean 80, which leads to...

(280+x)/5 = 80

280+x = 5*80

x+280 = 400

x = 400-280

x = 120

The fifth number is 120

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