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)

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difference = 31