SOLUTION: Some students set for a test. p students average mark was 70 and n students average mark was 92. When the test scores are added the average is 86. Find p and n.

Question 627207: Some students set for a test. p students average mark was 70 and n students average mark was 92. When the test scores are added the average is 86. Find p and n.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Some students set for a test. p students average mark was 70 and n students average mark was 92. When the test scores are added the average is 86. Find p and n.

Average of p students� scores = 70, so total score = 70p
Average of n students� scores = 92, so total score = 92n
Average of all scores = (70p + 92n)/(p + n)
86 = (70p + 92n)/(p + n)
86(p + n) = 70p + 92n ------ Cross-multiplying
86p + 86n = 70p + 92n
86p � 70p = 92n � 86n
16p = 6n
2(8p) = 2(3n)---- Factoring out GCF, 2
8p = 3n

Since 8p = 3n, then 8(3) = 3(8)

This means that , and

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Check
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3 students� average score = 70 for a total score of 210
8 students� average score = 92 for a total score of 736
Average of all students� scores = , or , or 86 (given)

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