Vincen wrote: ↑

Tue Oct 06, 2020 7:06 am

Seven friends went to an art festival and each spent a different sum of money. If the friends' totals were \(\$127, \$135, \$129, \$138, \$126, \$142,\) and \(\$134,\) what was the average sum of money that a friend spent?

A. \(\$128\)
B. \(\$133\)
C. \(\$138\)
D. \(\$141\)
E. \(\$145\)

Answer: B

Solution:

Sum/quantity = average, so we have:

(127 + 135 + 129 + 138 + 126 + 142 + 134) / 7 = 931/7 = $133

Alternate Solution:

Let’s pick a value that is close to all the sums, such as 130. We will add the signed differences between the sums and 130:

(127 - 130) + (135 - 130) + (129 - 130) + (138 - 130) + (126 - 130) + (142 - 130) + (134 - 130)

-3 + 5 + (-1) + 8 + (-4) + 12 + 4 = +21

So, the average of all the sums differs from 130 by 21/7 = +3; therefore, the average is 130 + 3 = $133. Note that we would have obtained the same answer had we calculated the differences with a different number, such as 125 or 135.

Answer: B