SOLUTION: In a business studies test, 30 more students passed than the number of those that failed. In the next test, 7 students who passed the first test, failed & 1/3 of those who failed p
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Question 305760: In a business studies test, 30 more students passed than the number of those that failed. In the next test, 7 students who passed the first test, failed & 1/3 of those who failed passed. As a result, 31 more passed the second test than failed on it.What was the record of passing or failing on the first test? Please help with the equations & the solution. Thanks! Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Let x = no. that originally passed
Let y = no. that originally failed
:
"In a business studies test, 30 more students passed than the number of those that failed."
x - y = 30
:
"In the next test, 7 students who passed the first test, failed & 1/3 of those who failed passed."
(x-7) passed this test y passed this test
then y failed this time
:
" As a result, 31 more passed the second test than failed on it."
(x-7) - y = 31
multiply by 3
3(x-7) - 2y = 3(31)
3x - 21 - 2y = 93
3x - 2y = 93 + 21
3x - 2y = 114
:
Use elimination on the 1st and 2nd test equations, multi the 1st eq by 2
3x - 2y = 114
2x - 2y = 60
-----------------subtraction eliminates y, find x
x = 54 originally passed
Find y
54 - y = 30
54 - 30 = y
y = 24 originally failed
:
:
Confirms these solutions in the statements:
" 7 students who passed the first test, failed & 1/3 of those who failed passed.
As a result, 31 more passed the second test than failed on it."
(54-7) - (24) =
47 - 16 = 31
