document.write( "Question 1204798: Hi
\n" ); document.write( "There were 2 classes A and B. 3/4 of the students in A and 5/8 in B passed a test. An equal number of students in both classes failed the test. If there was a total of 84 passes,what was the total number of students in both classes.
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Algebra.Com's Answer #841296 by math_tutor2020(3817) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Class A: 3/4 passed, 1/4 failed
\n" ); document.write( "Class B: 5/8 passed, 3/8 failed\r
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\n" ); document.write( "\n" ); document.write( "x = number of students in class A
\n" ); document.write( "y = number of students in class B\r
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\n" ); document.write( "\n" ); document.write( "(1/4)x = number in class A that failed
\n" ); document.write( "(3/8)y = number in class B that failed
\n" ); document.write( "(1/4)x = (3/8)y
\n" ); document.write( "4*(1/4)x = 4*(3/8)y
\n" ); document.write( "x = 1.5y
\n" ); document.write( "We'll use this in a substitution step later.\r
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\n" ); document.write( "\n" ); document.write( "(3/4)x = number in class A who passed
\n" ); document.write( "(5/8)y = number in class B who passed
\n" ); document.write( "(3/4)x+(5/8)y = total number of passing grades
\n" ); document.write( "(3/4)x+(5/8)y = 84
\n" ); document.write( "8*((3/4)x+(5/8)y) = 8*84
\n" ); document.write( "6x+5y = 672\r
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\n" ); document.write( "\n" ); document.write( "Plug in the previous equation we found earlier.
\n" ); document.write( "6x+5y = 672
\n" ); document.write( "6*1.5y+5y = 672
\n" ); document.write( "9y+5y = 672
\n" ); document.write( "14y = 672
\n" ); document.write( "y = 672/14
\n" ); document.write( "y = 48 people in class B
\n" ); document.write( "(3/8)y = (3/8)*48 = 18 people in class B failed the test, and it's also the number of people who failed in class A.\r
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\n" ); document.write( "\n" ); document.write( "There are 48-18 = 30 people who passed in class B.\r
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\n" ); document.write( "\n" ); document.write( "(1/4)x = number who failed class A's test
\n" ); document.write( "(1/4)x = 18
\n" ); document.write( "x = 4*18
\n" ); document.write( "x = 72 people in class A
\n" ); document.write( "72 - 18 = 54 people passed in class A
\n" ); document.write( "Or we could write it as:
\n" ); document.write( "(3/4)x = (3/4)*72 = 54 people passed in class A\r
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\n" ); document.write( "\n" ); document.write( "Ultimately there are x+y = 72+48 = 120 students total\r
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\n" ); document.write( "\n" ); document.write( "Summary Table
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	Class A	Class B	Total
Passed	54	30	84
Failed	18	18	36
Total	72	48	120

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