1999 CEMC Pascal Problems/Problem 19

Problem

The numbers $49, 29, 9, 40, 22, 15, 53, 33, 13, 47$ are grouped in pairs so that the sum of each pair is the same. Which number is paired with $15$ ?

$\text{ (A) }\ 33 \qquad\text{ (B) }\ 40 \qquad\text{ (C) }\ 47 \qquad\text{ (D) }\ 49 \qquad\text{ (E) }\ 53$

Solution

Let $x$ be the number that is paired with $15$ .

Since there are $10$ numbers, there are $\frac{10}{2} = 5$ pairs in total. This means that we can find the total sum of the numbers and divide it by $5$ to get the sum of each pair:

$\frac{49 + 29 + 9 + 40 + 22 + 15 + 53 + 33 + 13 + 47}{5}$

$=\frac{310}{5} = 62$

We can now set up an equation involving $x$ and $15$ :

$x + 15 = 62$

$x = 62 - 15 = 47$

~anabel.disher

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1999 CEMC Pascal Problems/Problem 19

Problem

Solution