On Monday, a person mailed 8 packages

On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 12 3/8 pounds, and on Tuesday, 4 packages weighing an average of 15 1/4 pounds. What was the average weight, in pounds, of all packages the person mailed on both days?

2 Explanations

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Shortcut: Note that the number of packages mailed on Monday is exactly double the number of packages mailed on Tuesday. Hence the average of Monday counts twice as much as the average on Tuesday in calculating the weighing average. To calculate simply double the average of monday (2 * 12 3/8 = 24 3/4) and add to one average of Tuesday (24 3/4 + 15 1/4 = 40). Divide this sum by 3 to get 13 1/3.

Sep 17, 2014 • Comment

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Mike McGarry, Magoosh Tutor

Dec 26, 2013 • Comment

Christina Lee

Could you explain the steps of multiplying 8 and 12^(3/8) to arrive at 99? As well as the process of multiplying 4 by (15 raised to the 1/4 power) equaling 61. I cannot recall the fractional exponent rule...thanks!

Nov 12, 2018 • Reply

Adam

Hey Christina, there aren't actually any exponents here. 12 3/8 is just a mixed number: an integer plus a fraction, and it is simply multiplied by 8. To do that multiplication, it might be helpful to break it up. So 8 times 12 is 96, and 8*(3/8) = 24/8 = 3. Add them together and we get 96+3 = 99. Similarly, 4*15 = 60 and 4*(1/4) = 1, so 4*(15 1/4) = 61.

Nov 12, 2018 • Reply

Christina Lee

Thank you for catching my error!

Nov 12, 2018 • Reply

Adam

You're welcome, sometimes it's hard to keep everything straight when it's in plain text!

Nov 12, 2018 • Reply