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Chapter 12: Problem 7

Towns \(A, B, C,\) and \(D\) are all in the same voting district. Towns \(A\) and \(B\) have 3,000 people each who support referendum \(R\) and the referendum has an average (arithmetic mean) of 3,500 supporters in towns \(B\) and \(D\) and an average of 5,000 supporters in Towns \(A\) and \(C.\) Quantity \(\mathbf{A}\) The average number of supporters of Referendum \(R\) in Towns \(C\) and \(D\) Quantity \(\underline{B}\) The average number of supporters of Referendum \(R\) in Towns \(B\) and \(C\) A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal, D. The relationship cannot be determined from the information given.

Short Answer

Expert verified
A. Quantity A is greater.

Step by step solution

01

Determine the supporters in towns B and D

The average number of supporters for towns B and D is 3,500. Therefore, considering that the number of supporters in town B is 3,000, the number of supporters in town D can then be calculated by multiplying the average by 2 (because there are two towns) and then subtracting the known number of supporters in town B. This gives: \(2*3500 - 3000 = 4000\), so there are 4,000 supporters in town D.
02

Determine the supporters in towns A and C

The average number of supporters for towns A and C is 5,000. Since we know the number of supporters in town A is 3,000, we can get the number of supporters in town C by a similar approach to Step 1. \(2*5000 - 3000 = 7000\), thus there are 7,000 supporters in town C.
03

Calculate Quantity A and Quantity B

In this step, we calculate Quantity A which is the average number of supporters in towns C and D. This is easy now as we add the supporters in town C and D then divide by 2. This gives us \((7000+4000)/2 = 5500\), so Quantity A is 5500. Quantity B which is the average number of supporters in towns B and C can also be calculated in a similar way. This gives \((3000+7000)/2 = 5000\), therefore Quantity B is 5000.
04

Compare Quantities A and B

Now with Quantity A as 5500 and Quantity B as 5000, Quantity A is greater than Quantity B

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Most popular questions from this chapter

One ounce of Solution \(X\) contains only ingredients \(a\) and \(b\) in a ratio of \(2: 3 .\) One ounce of Solution \(Y\) contains only ingredients \(a\) and \(b\) in a ratio of \(1: 2 .\) If Solution \(Z\) is created by mixing solutions \(X\) and \(Y\) in a ratio of \(3: 11,\) then 630 ounces of Solution \(Z\) contains how many ounces of \(a ?\) A. $$68$$ B. $$73$$ C. $$89$$ D. $$219$$ E. $$236$$

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