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Suppose that 6% of the eighth graders and 3% of the seventh graders at Washington Junior High participate in MATHCOUNTS. There are 2 times as many 8th graders as 7th graders at the school. What percentage of the 7th and 8th graders, taken together, participate i

 Aug 4, 2020
 #1
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Let N be the number of seventh-graders.....then, 1.5N = the number of eigth--graders....so we have

 

[.06(1.5)N + .03(N)] / [N + 1.5N]  =

 

[.09N + .03N] / [ 2.5N]  =

 

[.12N] / [2.5N]  =     ["cancel" the "N's" ]

 

.12/2.5 =  .048  =  4.8% 

 Aug 4, 2020
 #2
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N = 7th graders

2N = 8th graders

 

[.06 (2N) + .03(N) ] / 3N =  [.12 +.03]/3 = .05 =  5% of total students

 Aug 4, 2020

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