document.write( "Question 718456: I think I have the right answer, but I can't remember how to \"show\" the work / explain how I got the answer! \r
\n" ); document.write( "\n" ); document.write( "You get a mark of 80% on the first test, and the average of the marks of the first two tests is 15% higher than the mark on the last one. The average of all marks is 70%. What are the marks of all three tests.\r
\n" ); document.write( "\n" ); document.write( "By looking at the question, it appears that the first two test marks are 80 + 70 = 150 /2 = 75%
\n" ); document.write( "Therefore, the remaining mark is 60%, which is 15% less than the average of the first two.
\n" ); document.write( "(and 80 + 70 + 60) = 70% average / 210 total percent over 3 tests.\r
\n" ); document.write( "\n" ); document.write( "However, I just managed to get the answer from this simple question by \"looking\" at it.
\n" ); document.write( "Would somebody please teach me how to \"properly\" solve it so that I can understand & solve more complicated variations in the future? \n" ); document.write( "
Algebra.Com's Answer #440912 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
You get a mark of 80% on the first test, and the average of the marks of the first two tests is 15% higher than the mark on the last one.
\n" ); document.write( " The average of all marks is 70%. What are the marks of all three tests.
\n" ); document.write( ":
\n" ); document.write( "Looking at your answer, I noticed that 75 is not 15% more than 60, anyway
\n" ); document.write( ":
\n" ); document.write( "Let x = the mark on the third test
\n" ); document.write( "then
\n" ); document.write( "\"the average of the marks of the first two tests is 15% higher than the mark on the last one\"
\n" ); document.write( "2(1.15x) = total marks on the 1st two tests
\n" ); document.write( ":
\n" ); document.write( "\"%282%281.15x%29+%2B+x%29%2F3\" = 70
\n" ); document.write( "2.30x + x = 3(70)
\n" ); document.write( "3.30x = 210
\n" ); document.write( "x = 210/3.3
\n" ); document.write( "x = 63.64, his grade on the third test
\n" ); document.write( ":
\n" ); document.write( "Then
\n" ); document.write( "1.15(63.64) = 73.18 is the average on the 1st two test
\n" ); document.write( ":
\n" ); document.write( "Find the mark on the 2nd test, call it y:
\n" ); document.write( "\"%2880%2By%29%2F2\" = 73.18
\n" ); document.write( "80+y = 2(73.18)
\n" ); document.write( "y = 146.36 - 80
\n" ); document.write( "y = 66.36 is the grade on the 2nd test
\n" ); document.write( ":
\n" ); document.write( " What are the marks of all three tests. 80, 66.36, 63.64
\n" ); document.write( ":
\n" ); document.write( "See if this works out
\n" ); document.write( "av = \"%2880+%2B+66.36+%2B+63.64%29%2F3\"
\n" ); document.write( "av = \"210%2F3\" = 70
\n" ); document.write( "and find 15% more than the 3rd grade
\n" ); document.write( "1.15(63.64) = 73.2 which is the average of 80 and 66.36
\n" ); document.write( " \n" ); document.write( "
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