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Question 926:



No answer provided yet.To solve this we need to use a little bit of Algebra and work backwards from the weighted mean formula. The weighted mean is found by multiplying the average of each group by the total number in that group, then dividing that value by the total number in each group.

We are missing information on the number of boys so we will use x in place of that number. Then we isolate x on one side of the equation which will tell us the total number of boys.

9.7(20) +11.1(x) / 20 + x  = 10.3

We do a cross-product multiplication to isolate x.

10.3(20+x) = 9.7(20) +11.1(x)

Let's simplify the equation by distributing 10.3 and multiplying out 9.7 and 20. We now get
206 +10.3x = 194 +11.1x

Now let's get the x's on one side of the equals sign by subtracting terms.

12 = .8x

Finally we divide both sides by .8.

x = 15

So our equation tells us that there are 15 boys. We can double check this by substituting this back into the weighted mean equation.

9.7(20) +11.1(15) / 20 + 15  = 10.3

194+166.5 / 35 = 10.3

10.3 = 10.3

And we see that 15 does work.

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