# Thread: SAT math question (averages)

1. ## SAT math question (averages)

Each of 5 people had a blank card on which they wrote a positive integer. If the average (arithmetic mean) of these integers is 15, what is the greatest possible integer that could be on one of the cards?

The correct answer is 71.

I know that the total sum of these integers is 75, because 5 * 15 = 75; but I don't know what to do from here.

2. Originally Posted by Pn0yS0ld13r
Each of 5 people had a blank card on which they wrote a positive integer. If the average (arithmetic mean) of these integers is 15, what is the greatest possible integer that could be on one of the cards?

The correct answer is 71.

I know that the total sum of these integers is 75, because 5 * 15 = 75; but I don't know what to do from here.
The average is in real, not integer, terms, so there is a difference between 15 and 15.2! Therefore, taking four other cards at the lowest value (let's assume that is 1), then we have:

$\displaystyle \frac{X+4}{5}=15$

Solving for X gives us 71.

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### each of 5 people had a blank card on which they wrote a positive integer

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