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Question
Max has a box of 200 colored blocks. The box has an equal number of green and blue blocks and an equal number of red and yellow blocks. If Max arranged all of the green blocks in stacks of 12 and all of the blue blocks in stacks of 7, how many red blocks are in the box?
Responses
To find the number of red blocks in the box, we need to determine the number of green and blue blocks first. It is mentioned that the box has an equal number of green and blue blocks.
Let's use algebra to solve this problem.
Let's assume the number of green and blue blocks in the box is "x".
Since green blocks are arranged in stacks of 12, the total number of green blocks can be represented as 12x.
Similarly, since blue blocks are arranged in stacks of 7, the total number of blue blocks can be represented as 7x.
Summing up both green and blue blocks:
Total number of blocks = 12x + 7x
From the information given, it is mentioned that the box has 200 colored blocks. Therefore, we can equate the total number of blocks to 200:
12x + 7x = 200
Combining like terms:
19x = 200
Solving for x:
x = 200 / 19
x ≈ 10.526
Since the number of blocks cannot be a fraction, we can round down to the nearest whole number. Therefore, x = 10.
So, there are 10 green and 10 blue blocks in the box.
Now, let's find the number of red blocks.
The number of red blocks is equal to the number of blue blocks, which is 10.
Hence, there are 10 red blocks in the box.