I have more than 9 but less than 16 marbles.
There are half as many red as blue. There
are two more green than blue. There is an
odd number of yellow. What do I have
To solve this problem, let's break it down step by step:
Step 1: Determine the number of marbles you have.
Based on the given information, you have more than 9 but less than 16 marbles. So, the possible options are 10, 11, 12, 13, 14, or 15 marbles.
Step 2: Determine the number of red marbles.
The number of red marbles is half the number of blue marbles. Let's consider the possible number of blue marbles one by one.
If you have 10 blue marbles, then you have 5 red marbles (half of 10).
If you have 11 blue marbles, then you have 5.5 red marbles, but since we can only have whole numbers of marbles, this is not possible.
If you have 12 blue marbles, then you have 6 red marbles.
If you have 13 blue marbles, then you have 6.5 red marbles, which is not a whole number and is not possible.
If you have 14 blue marbles, then you have 7 red marbles.
If you have 15 blue marbles, then you have 7.5 red marbles, which is not a whole number and is not possible.
Step 3: Determine the number of green marbles.
The number of green marbles is two more than the number of blue marbles. Again, let's consider the possible number of blue marbles one by one.
If you have 10 blue marbles, then you have 12 green marbles (10 + 2).
If you have 12 blue marbles, then you have 14 green marbles (12 + 2).
If you have 14 blue marbles, then you have 16 green marbles (14 + 2).
Since we want to have fewer than 16 marbles, having 14 blue marbles (and 16 green marbles) is not possible.
Step 4: Determine the number of yellow marbles.
There is an odd number of yellow marbles. Based on the given information, we know that the other three colors (red, blue, and green) have even numbers, so if there is an odd number of marbles, it must be attributed to the yellow marbles.
Step 5: Summarize the results.
Based on the previous steps, the only possible solution is: 10 blue marbles, 5 red marbles, 12 green marbles, and an odd number of yellow marbles.
So, you have 10 blue marbles, 5 red marbles, 12 green marbles, and an odd number of yellow marbles.