A box contained some red, blue, and green markers. For every 5 red markers, there were 2 blue markers. For every 3 blue markers, there were 5 green markers.

a. Find the ratio of red markers to blue markers to green markers.

b. When 6 red markers were removed from the box,3/7 of the remaining markers were red markers. How many markers were left in the box?

To find the ratio of red markers to blue markers to green markers, we need to determine the relationship between the number of markers of each color.

We are given the following relationships:
For every 5 red markers, there were 2 blue markers.
For every 3 blue markers, there were 5 green markers.

Step 1: Determine the number of blue markers in terms of red markers.
Since there are 2 blue markers for every 5 red markers, the ratio of red markers to blue markers can be simplified as 5:2.

Step 2: Determine the number of green markers in terms of blue markers.
Since there are 5 green markers for every 3 blue markers, the ratio of blue markers to green markers can be simplified as 3:5.

Step 3: Combine the two ratios to find the overall ratio of red markers to blue markers to green markers.
Multiplying the first ratio (5:2) with the second ratio (3:5), we get the overall ratio of red markers to blue markers to green markers as 15:6:10.

Answer to a: The ratio of red markers to blue markers to green markers is 15:6:10.

To solve part b, we need to find the number of markers left in the box after 6 red markers are removed and 3/7 of the remaining markers are red markers.

Step 1: Let's assume the number of red markers in the box is R.

Step 2: After removing 6 red markers, the number of red markers left in the box is R - 6.

Step 3: The total number of remaining markers in the box is given by (3/7)(R - 6). According to the problem, this value should equal the number of red markers remaining.

Step 4: Set up the equation (3/7)(R - 6) = R - 6.

Step 5: Solve the equation to find the value of R.

Starting with step 4: (3/7)(R - 6) = R - 6.
Expanding the left side: (3/7)R - 18/7 = R - 6.
Multiply both sides by 7 to get rid of the fraction: 3R - 18 = 7R - 42.
Subtract 3R from both sides: 7R - 3R - 18 = 7R - 3R - 42.
Combine like terms: 4R - 18 = -42.
Add 18 to both sides: 4R - 18 + 18 = -42 + 18.
Simplify: 4R = -24.
Divide both sides by 4: 4R/4 = -24/4.
Simplify: R = -6.

Step 6: Check the answer.
Since the number of markers cannot be negative, we must discard the negative solution.
Therefore, we conclude that there were no markers left in the box.

Answer to b: There were no markers left in the box after removing 6 red markers.

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