max has a box of 200 colored blocks. the box has an equal number of green and blue blocks and 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 key on USA test prep

Question

max has a box of 200 colored blocks. the box has an equal number of green and blue blocks and 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 key on USA test prep

Answer 1

The answer is 16

Answer 2

To find the number of red blocks in the box, we need to use the given information.

We know that there are an equal number of green and blue blocks. Let's assume the number of green and blue blocks is 'x'.

Therefore, the number of green blocks is 'x', and the number of blue blocks is also 'x'.

Next, we need to determine the number of red blocks. We know that the total number of blocks in the box is 200.

So, the total number of blocks can be expressed as: x (green) + x (blue) + y (red) + y (yellow) = 200, where y is the number of red and yellow blocks.

Since the numbers of green and blue blocks are equal (both 'x'), we can rewrite the equation as: 2x + 2y = 200.

Now, let's focus on the more specific information given in the question. Max arranged all of the green blocks in stacks of 12 and all of the blue blocks in stacks of 7.

To find the number of red blocks, we need to determine the value of 'x'. Let's solve the equation to find the value of 'x'.

2x + 2y = 200

We can simplify this equation further by dividing it by 2:

x + y = 100

Now, let's consider the information about the stacks. Max arranged all of the green blocks in stacks of 12, so the number of green blocks must be a multiple of 12. Similarly, all of the blue blocks were arranged in stacks of 7, so the number of blue blocks must be a multiple of 7.

That means the value of 'x' (the number of green and blue blocks) must be a common multiple of 12 and 7.

The least common multiple (LCM) of 12 and 7 is 84.

So, we can substitute 'x' with 84 in the equation:

84 + y = 100

Simplifying, we find:

y = 100 - 84
y = 16

Therefore, there are 16 red blocks in the box.

Answer 3

If there are x blue and x green,

we know that x must be LCM(12,7) = 84
then there are (200-84*2)/2 red and yellow

max has a box of 200 colored blocks. the box has an equal number of green and blue blocks and 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 key on USA test prep

The answer is 16

To find the number of red blocks in the box, we need to use the given information.

tysm!!!

If there are x blue and x green,