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You can put this solution on YOUR website!
2/3 * 48 = 32
\n" ); document.write( "let x = grade she has to get on final.
\n" ); document.write( "since the final counts as 1/3, then x/3 is what she needs to get.
\n" ); document.write( "32 + x/3 = 70 would be the low score
\n" ); document.write( "32 + x/3 = 79 would be the high score.
\n" ); document.write( "---
\n" ); document.write( "going for the low score:
\n" ); document.write( "32 + x/3 = 70
\n" ); document.write( "x/3 = 70 - 32 = 38
\n" ); document.write( "x = 3 * 38 = 114
\n" ); document.write( "she would need to get a 114 on the test to get a grade of 70.
\n" ); document.write( "forget 79.
\n" ); document.write( "she can't even get 70.
\n" ); document.write( "---
\n" ); document.write( "something is wrong with the question.
\n" ); document.write( "i suspect you meant:
\n" ); document.write( "midterm counts as 1/3
\n" ); document.write( "final counts as 2/3
\n" ); document.write( "---
\n" ); document.write( "going on that assumption, i'll try to solve again.
\n" ); document.write( "---
\n" ); document.write( "she got 48 on the midterm and that counts as 1/3 of the total score.
\n" ); document.write( "1/3 * 48 = 16
\n" ); document.write( "since the final counts as 2/3 of the grade (under the new assumption), that means that 2/3 * x + 16 = 70 in order to obtain the low threshold requested.
\n" ); document.write( "subtract 16 from both sides to get:
\n" ); document.write( "2/3 * x = 54
\n" ); document.write( "divide both sides by 2/3 to get:
\n" ); document.write( "x = 54 / (2/3) = 54 * (3/2) = 81.
\n" ); document.write( "she would need to get an 81 on the final to average a 70 for the whole course.
\n" ); document.write( "---
\n" ); document.write( "81 is what she would need on the final to get the low score of 70.
\n" ); document.write( "---
\n" ); document.write( "the high score would be 79.
\n" ); document.write( "in order to get 79, the equation becomes:
\n" ); document.write( "2/3 * x + 16 = 79
\n" ); document.write( "subtract 16 from both sides to get:
\n" ); document.write( "2/3 * x = 63
\n" ); document.write( "divide both sides by 1/3 to get:
\n" ); document.write( "x = 63 / (2/3) = 63 * (3/2) = 94.5
\n" ); document.write( "she would need to get a 94.5 on the final to average a 79 for the whole course.
\n" ); document.write( "---
\n" ); document.write( "to prove these numbers are good, substitute in the original equations to see if the values hold up.
\n" ); document.write( "---
\n" ); document.write( "low score validation:
\n" ); document.write( "x = 81 = score on the final.
\n" ); document.write( "1/3 * 48 + 2/3 * 81 = 48/3 + 162/3 = 16 + 54 = 70
\n" ); document.write( "value of 81 on the final is good in order to obtain the low threshold of 70 in the course.
\n" ); document.write( "---
\n" ); document.write( "high score validation:
\n" ); document.write( "x = 94.5 = score on the final.
\n" ); document.write( "1/3 * 48 + 2/3 * 94.5 = 48/3 + 189/3 = 16 + 63 = 79
\n" ); document.write( "value of 94.5 on the final is good in order to obtain the high threshold of 79 in the course.
\n" ); document.write( "---
\n" ); document.write( "answer to the question is:
\n" ); document.write( "wendy has to get between 81 and 94.5 on the final in order to get a final average of 70 to 79, assuming the final score is 2/3 of the total score and the midterm score is 1/3 of the total score.
\n" ); document.write( "---
\n" ); document.write( "a reminder:
\n" ); document.write( "i changed the requirements because what you had originally stated (2/3 on the midterm and 1/3 on the final) didn't work. \n" ); document.write( "