SOLUTION: Could you please help me with this problem. Thanks in advance. On an algebra test 39 more pupils passed than failed. On a new test, 7 who had passed the first test failed, an

Question 112029: Could you please help me with this problem. Thanks in advance.
On an algebra test 39 more pupils passed than failed. On a new test,
7 who had passed the first test failed, and one third of those who
failed on the first test passed the second test. As a result, 31 more
passed the second test than failed it. What was the record of passing
and failing on the first test?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an expression for each statement:
:
Let x = number of students that originally failed
:
On an algebra test 39 more pupils passed than failed.
(x+39) = number of students that passed originally
:
On a new test,
7 who had passed the first test failed,
(x+39) - 7
x + 32 = Students who passed new test (from those that passed the 1st test)
:
and one third of those who failed on the first test passed the second test.
x = students who failed, passed the new test
:
As a result, 31 more passed the second test than failed it. What was the record of passing and failing on the first test?
:
Total passing of the 2nd test:
x + (x+32)
x + 32
:
Total failed the 2nd test:
x + 7
;
2nd test
Passed - failed = 31
x + 32 - (x + 7) = 31
x + 32 - x - 7 = 31
x + 25 = 31
x = 31 - 25
x = 6
2x = 3 * 6
2x = 18
x = 9 failed originally
then
9 + 39 = 48 passed originally
:
:
Check solution on the new test data:
12 + 32 = 44 passed (x + 32)
6 + 7 = 13 failed (x + 7)
--------------
difference = 31
:

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