There are some marbles in a box 1 6 of them are red 1 3 are blue and 3 7 of the remainder are green if there are 27 green marbles how many marbles are there together?
If 3/7 of the remainder are green, then the remainder is equal to 7/3 * 27 = <<3*27/7=11>>11.
The total number of marbles in the box is 27 + 11 = <<27+11=38>>38. Answer: \boxed{38}.
Let's break down the information provided step-by-step:
1. The box contains some marbles.
2. 6/13 of the marbles are red.
3. 1/3 of the marbles are blue.
4. The remainder (after the red and blue marbles) are green.
5. 3/7 of the remainder are green.
6. There are 27 green marbles.
To find the total number of marbles, we need to find the total number of each color and then add them together.
Step 1: Find the number of red marbles.
Let's set up an equation to find the number of red marbles:
6/13 * Total Marbles = Number of red marbles
6/13 * Total Marbles = Number of red marbles
Total Marbles = (Number of red marbles * 13) / 6
Step 2: Find the number of blue marbles.
Similarly, let's find the number of blue marbles:
1/3 * Total Marbles = Number of blue marbles
Total Marbles = Number of blue marbles * 3
Step 3: Find the number of remainder marbles (green marbles + remainder).
Let's set up an equation:
Total Marbles = Green marbles + Remainder marbles
Total Marbles = 27 + Remainder marbles
Step 4: Find the number of remainder marbles.
Let's use the given information: 3/7 of the remainder are green.
3/7 * Remainder marbles = 27
Remainder marbles = (27 * 7) / 3
Step 5: Calculate the total number of marbles.
Now, we can calculate the total number of marbles by adding the number of red marbles, blue marbles, green marbles, and the remainder marbles:
Total Marbles = (Number of red marbles * 13) / 6 + Number of blue marbles * 3 + Green marbles + Remainder marbles
By plugging in the values from the previous steps, we can find the total number of marbles.
To find the total number of marbles, we need to determine the number of green marbles and the remainder.
Let's start by calculating the remainder first. We know that 3/7 of the remainder are green, so we can set up the equation:
3/7 * remainder = 27
To solve for the remainder, we can multiply both sides of the equation by 7/3:
remainder = (27 * 7) / 3 = 63
Now we know that the remainder is 63.
Let's find the total number of marbles in the box. We have:
1/6 are red marbles
1/3 are blue marbles
3/7 are green marbles
remainder = 63
To get the total, we add all the fractions together:
1/6 + 1/3 + 3/7 + remainder = total number of marbles
To simplify the fractions, we can find a common denominator. The common denominator of 6, 3, and 7 is 42.
Now we rewrite each fraction with a denominator of 42:
7/42 + 14/42 + 18/42 + 63/42 = total number of marbles
Adding these fractions together, we find:
(7 + 14 + 18 + 63) / 42 = total number of marbles
92/42 = total number of marbles
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
(46/21) * (2/2) = total number of marbles
92/42 = 2.19
Therefore, the total number of marbles is approximately 2.19.