SOLUTION: Research shows that 14% of 6th graders in K-6 schools have tried cigarettes and 61% of 7th graders in 8-9 or 7-9 middle schools have tried cigarettes. what is the absolute increase

Question 1144273: Research shows that 14% of 6th graders in K-6 schools have tried cigarettes and 61% of 7th graders in 8-9 or 7-9 middle schools have tried cigarettes. what is the absolute increase to the nearest percent?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
i believe the increase would be calculated as follows:
(61% - 14%) / 14% = 47% / 14% = 3.357142857 * 100 = 335.7142857% increase.

let x equal the number of kindergarten through 6th graders.
let y equal the number of 7th to 9th graders.,

the number of kindergarten through 6th graders who have tried cigarettes would be .14 * x.

if there were no increase, the number of 7th to 9th graders who tried cigarettes would be .14 * y.

however, the number of 7th to 9th graders who tried cigarettes was .61 * y.

the increase is therefore (.61 * y - .14 * y) / (.14 * y) = .47 * y / .14 * y = .47 / .14 = 3.357142857 * 100 = 335.7142857%.

bear in mind that the number of 7th to 9th graders is not the same number as the number of kindergarten to 6th graders.

the percentages are applied to different base numbers.

that's why you need to set the base case for percentage of 7th to 9th graders.

the base case is the number of 7th to 9th graders who tried cigarettes if there were no increase in the percentage.

an example:

assume 100 kindergarten to 6th graders and 500 7th to 9th graders.

14% of 100 = 14 students out of 100 who tried cigarettes in the 6th grade.l

14% of 500 = 70 students out of 500 who tried cigarettes in the 7th through 9th grade.
61% of 500 = 305 students out of 500 who tried cigarettes in the 7th through 9th grade.

that's an increase of 305 - 70 = 235 out of 500 students in the 7th through 9th grade.

that's equal to 235 / 500 = .47 * 100 = 47% increase.

47% / 14% = 3.357142857 times more = 335.7142857% more.

3.357142857 * 70 = 235 more for a total of 305 out of 500 7th through 9th grade students.

if you assume the number of student in kindergarten through 6th grade is the same number of students in 7th through 9th grade, then the problem becomes a lot simpler, even though you get the same answer.

assume the number of students in kindergarten through 6th grade is 500.
14% of 500 is 70.
when these students advance to 7th through 9th grade, 61% have tried cigarettes.
that would be 61% of 500 = 305.
the increase is 305 - 70 = 235.
235/70 = 3.357142857 more = 335.7142857% more.

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

The problem is posed   I N C O R R E C T L Y.

The correct and meaningful solution is not possible and a correct answer CAN NOT be obtained in the given frame and information.

Did I say something about a correct answer ?
We even can not talk about an answer, since the question itself is posed incorrectly . . .

So, what came with this post, is good only to throw it into a GARBAGE BOX.

Penalty to the author . . .

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