Math Word Problem Help

Question

A conductor notes that the number of mistakes her orchestra makes one week before performance is proportional to the length of the piece. One piece is 22 minutes, 30 second long and the conductor notices 18 mistakes one week before performance. Their next piece is 13 minutes, 50 seconds long. How many mistakes does the conductor expect there to be one week before performance? Round your answer to the nearest integer.

Answer 1

Just like your earlier question, you can set up a proportion to solve. First, though, let's translate the minutes and seconds into just minutes:

 

22 minutes and 30 seconds = 22 and 30/60 minutes = 22 and 1/2 minutes = 22.5 minutes

13 minutes and 50 seconds = 13 and 50/60 minutes = 13 and 5/6 minutes = 83/6 minutes

 

 

Now, set up a proportion and cross-multiply to solve for x = mistakes on the second piece:

 

(first piece's length) / (first piece's mistakes) = (second piece's length) / (second piece's mistakes)

22.5/18 = (83/6)/x

22.5x = (83/6)(18)

22.5x = 249

x = 11.07

 

The conductor expects there to be 11 mistakes.