January 2012 Brain Teaser Solution

Andy and Sandy had to take a make-up class in math over the summer, a two-month, self-paced course with a test at the end of each of 12 chapters. The course requires a 70% grade to pass.  In the first month, they both had difficulties with the concepts. Andy averaged 60% on his exams; Sandy averaged 50%. In the second month, Andy averaged 90% on his exams; Sandy averaged 80%.  While Sandy got a passing grade of 75% in the class;  Andy failed with 65%. How did Sandy pass while Andy flunked? 

Their grades were weighted averages.

This can be solved using guess-and-check or through using algebra.

Let x = # of tests in the first month, therefore 12 - x would be the # of tests in the second month.

so Andy's tests can be modeled with algebra using: .6x + .9(12 - x) = .65 (12)

.6x + 10.8 -.9x = 7.8

-.3x + 10.8 = 7.8

-.3x = -3

x = 10 and 12 - x = 2

so Andy took 10 tests in the first month and 2 in the second month.

10(60) + 2(90) = 780 divided by 12 = 65

Sandy's tests can be modeled using .5x + .8(12 - x) = .75(12)

.5x + 9.6 - .8x = 9

9.6 - .3x = 9

-.3x = -.6

x = 2

so Sandy took 2 tests in the first month and 10 in the second month

2(50) + 10(80) = 900 divided by 12 = 75