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 o​f the remaining markers were red markers. How many markers were left in the box?

I thought the question said 3/7 not 37 for b

a. To find the ratio of red markers to blue markers to green markers, we will start with the information given.

For every 5 red markers, there were 2 blue markers. This ratio can be simplified to 5:2.

For every 3 blue markers, there were 5 green markers. This ratio can be simplified to 3:5.

Now, to find the overall ratio of red markers to blue markers to green markers, we can combine these two ratios.

The common factor between the two ratios is 15. So, we will multiply the first ratio by 3 and the second ratio by 5 to get the same denominator.

The simplified ratio is:

(5 * 3) : (2 * 3) : (5 * 5)
15:6:25

Therefore, the ratio of red markers to blue markers to green markers is 15:6:25.

b. Let's use the information provided to solve this.

Initially, for every 5 red markers, there were 2 blue markers. So the box contained a total number of markers that is a multiple of both 5 and 2.

Let's assume that the box initially contained 10 red markers (5 * 2), 4 blue markers (2 * 2), and 10 green markers (5 * 2).

When 6 red markers were removed, we are left with 4 red markers (10 - 6).

We are told that 37 of the remaining markers were red markers, which means the total number of remaining markers is 37 red markers multiplied by the common factor between the three colors.

So, the total number of remaining markers can be calculated as follows:

Total remaining markers = 37 red markers * (15 (common factor)) = 555 markers.

Therefore, there were 555 markers left in the box.

To solve this problem, we will use a system of equations to represent the relationships given in the problem.

Let's say the number of red markers is represented by "r", the number of blue markers is represented by "b", and the number of green markers is represented by "g".

From the problem, we know that:
1. For every 5 red markers, there were 2 blue markers. This can be represented as:
r/b = 5/2

2. For every 3 blue markers, there were 5 green markers. This can be represented as:
b/g = 3/5

a. To find the ratio of red markers to blue markers to green markers, we need to find the values of r, b, and g. To do this, we can use the system of equations:

From equation 1, we can solve for b in terms of r:
b = (2/5) * r

Substituting this value of b in equation 2, we have:
((2/5) * r) / g = 3/5

Simplifying the equation, we get:
(2r) / (5g) = 3/5

Cross-multiplying, we get:
2r * 5 = 3 * 5g
10r = 15g
r = (15/10) * g
r = (3/2) * g

So, the ratio of red markers to green markers is 3:2.

Now, substituting the value of b in equation 1, we have:
r / ((2/5) * r) = 5/2
5r = (2/5) * r
5 = 2/5
25 = 2r
r = 25/2

So, the ratio of red markers to blue markers is 25:2.

Finally, substituting the value of r in the equation r = (3/2) * g, we have:
(3/2) * g = 25/2
3g = 25
g = 25/3

So, the ratio of blue markers to green markers is 2:25/3.

Therefore, the ratio of red markers to blue markers to green markers is 25:2:25/3.

b. To find the number of markers left in the box, we need to subtract the 6 red markers removed from the original number of red markers, and then find the total number of markers.

Given that 37 of the remaining markers are red, we can set up an equation:
(r - 6) = 37

Solving for r, we get:
r = 37 + 6
r = 43

Substituting the value of r in equation b = (2/5) * r, we have:
b = (2/5) * 43
b = 86/5

Similarly, substituting the value of r in equation g = (3/2) * r, we have:
g = (3/2) * 43
g = 129/2

Adding together the number of red, blue, and green markers, we get:
43 + 86/5 + 129/2 = (43*10 + 172 + 645)/10
= (430 + 172 + 645)/10
= 1247/10

Therefore, there were 1247/10 markers left in the box, or 124.7 markers (rounded to the nearest whole number).

r:b = 5:2

b:g = 3:5
or,

r:b = 15/6
b:g = 6:10
so, r:b:g = 15:6:10

so, see what you can do with part (b)