Question

stretch your thinking fifteen children voted for their favorite color. the votes for red and blue together were double the votes for green and yellow together. how did the children vote?

Explanation:

Step1: Set up equations

Let \(x\) be the number of votes for green and yellow together, and \(2x\) be the number of votes for red and blue together. Since the total number of votes is \(15\), we have \(x + 2x=15\).

Step2: Solve for \(x\)

Combine like - terms: \(3x = 15\). Then divide both sides by \(3\): \(x=\frac{15}{3}=5\). So the number of votes for green and yellow together is \(5\), and the number of votes for red and blue together is \(2x = 10\).

Step3: Find possible vote distributions

For red and blue (total \(10\) votes), possible distributions: \((6,4)\), \((7,3)\), \((8,2)\), \((9,1)\). For green and yellow (total \(5\) votes), possible distributions: \((1,4)\), \((2,3)\).

Let's assume one case:
If red \(= 6\), blue \(= 4\), green \(= 2\), yellow \(= 3\)

Answer:

Color	Votes
Blue	\(4\)
Green	\(2\)
Yellow	\(3\)

(Note: There are multiple correct answers. Another example: red \(= 7\), blue \(= 3\), green \(= 1\), yellow \(= 4\))