Question 112029
Write an expression for each statement:
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Let x = number of students that originally failed
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On an algebra test 39 more pupils passed than failed. 
(x+39) =  number of students that passed originally
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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)
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and one third of those who failed on the first test passed the second test. 
{{{1/3}}}x = students who failed, passed the new test
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As a result, 31 more passed the second test than failed it. What was the record of passing and failing on the first test?
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Total passing of the 2nd test: 
{{{1/3}}}x + (x+32)
{{{4/3}}}x + 32
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Total failed the 2nd test: 
{{{2/3}}}x + 7
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2nd test
Passed - failed = 31
{{{4/3}}}x + 32 - ({{{2/3}}}x + 7) = 31
{{{4/3}}}x + 32 - {{{2/3}}}x - 7 = 31
{{{2/3}}}x + 25 = 31
{{{2/3}}}x = 31 - 25
{{{2/3}}}x = 6
2x = 3 * 6
2x = 18 
x = 9 failed originally
then
9 + 39 = 48 passed originally
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Check solution on the new test data:
12 + 32 = 44 passed ({{{4/3}}}x + 32)
 6 + 7 =  13 failed ({{{2/3}}}x + 7)
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difference = 31
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