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.

Question

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, 37 of the remaining markers were red markers. How many markers were left in the box?

Answer 1

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Answer 2

To solve this problem, we will break it down into two parts:

Part 1: Finding the ratio of red, blue, and green markers.
Part 2: Using the information given in Part 1 to solve the second scenario.

Part 1: Finding the ratio of red, blue, and green markers.

In this problem, we are given the following information:

- For every 5 red markers, there are 2 blue markers.
- For every 3 blue markers, there are 5 green markers.

Let's assign variables to each quantity:
- Let's assume there are R red markers.
- Since there are 5 red markers for every 2 blue markers, we can say there are (2/5) * R blue markers.
- Since there are 3 blue markers for every 5 green markers, we can say there are (5/3) * ((2/5) * R) = (2/3) * R green markers.

Now we can calculate the ratio of red, blue, and green markers:
- The ratio of red markers to blue markers is R : (2/5) * R = 5 : 2
- The ratio of blue markers to green markers is (2/5) * R : (2/3) * R = 3 : 5

So, the ratio of red markers to blue markers to green markers is 5 : 2 : 5.

Part 2: Using the information to solve the second scenario.

In this scenario, we are told that 6 red markers were removed from the box, and 37 of the remaining markers are red.

Let's assume there were initially R red markers in the box, then after removing 6 red markers, there are (R - 6) red markers remaining.

According to the given information, 37 of these remaining markers are red. Therefore, we can write the equation:

(R - 6) = 37

Now, we can solve for R:

R = 37 + 6
R = 43

So, there were initially 43 red markers in the box.

To find the total number of markers left in the box, we need to calculate the sum of red, blue, and green markers:

Total markers = R + (2/5) * R + (2/3) * ((2/5) * R)

Substituting the value of R, we get:

Total markers = 43 + (2/5) * 43 + (2/3) * ((2/5) * 43)

Now, you can simplify the expression to find the total number of markers left in the box.