My 7-year-old has a "Stretch your thinking" question in her homework that baffles me in terms of explaining how to solve it.
Up to this point her class has only studied addition and subtraction.
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?
There is also a table that looks like this:
Color | Votes Red Blue Green Yellow
I don't know how I would explain this except to say that she should start with the green + yellow set having 1, then the red + blue set would have 2, and the total is 3. That isn't fifteen so she should try again, starting with green + yellow set having 2 (adding one to initial set) until she gets to a total that equals 15.
Is there a better way to explain it?
Best Answer
There’s nothing wrong with intelligently directed trial and error. Point out that every vote for green or yellow can be matched up with two votes for red or blue, as in the following chart:
$$\begin{array}{rcc} \text{green or yellow}:&*&*&*&*&*\\ \text{red or blue}:&*\atop*&*\atop*&*\atop*&*\atop*&*\atop*\\ \text{total votes so far}:&3&6&9&12&\color{red}{15} \end{array}$$
When the magic number $15$ is reached we can go back and count the green or yellow votes ($5$) and the red or blue votes ($10$). You can point out that as a check, $5+5=10$, so there really are twice as many votes for red or blue as for green or yellow.