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

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

RELATED QUESTIONS
Average score of 120 students in a test is 35 (out of 50). The average scores of students (answered by SmithWillSuffice)

Could you please help me with this problem. Thanks in advance. On an algebra test 39... (answered by ankor@dixie-net.com)

In a class, 85% of the students passed a test. 40% of the students who failed the test... (answered by Theo,ikleyn)

In a math class with 27 students, a test was given the same day that an assignment was... (answered by Boreal)

In a math quiz, the average score of a class of 28 students is 82. The average of those... (answered by rothauserc,greenestamps)

78 students took a test. 2 students failed the test. What percent of the students passed... (answered by Fombitz,stanbon)

a class of 38 students took two tests in local history. 32 students passed test 1 and 34... (answered by ikleyn)

Mr. Taylor gave his class a test the day after spring break. The average score for all... (answered by stanbon)

please help me solve this question: If 13 out of 30 students failed a math test. What is (answered by richwmiller)