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.
Let's assume the total number of marbles is x.
The number of red marbles is 1/6 * x.
The number of blue marbles is 1/3 * x.
The number of green marbles is 3/7 of the remainder, so it is 3/7 * (x - (1/6 * x) - (1/3 * x)).
We are given that there are 27 green marbles, so we can write the equation:
3/7 * (x - (1/6 * x) - (1/3 * x)) = 27
Simplifying the equation, we get:
3/7 * (6/6 - 1/6 - 2/6) * x = 27
3/7 * (3/6) * x = 27
9/42 * x = 27
9x = 27 * 42
9x = 1134
x = 1134/9
x = 126
Therefore, there are a total of 126 marbles.
Let's solve this problem step-by-step:
Step 1: Find the total fraction of green marbles
The given information states that 3/7 of the remaining marbles are green. Let's represent the total number of remaining marbles as x. So, we can say that (3/7) * x = 27.
Step 2: Solve for x
To find the value of x, we can multiply both sides of the equation by 7/3:
x = 27 * (7/3)
x = 63
Step 3: Find the total number of marbles
To find the total number of marbles, we need to add the number of red, blue, and green marbles. Given that 1/6 are red and 1/3 are blue, we can calculate as follows:
Number of red marbles = (1/6) * 63 = 10.5 (since we can't have half a marble, we'll round this down to 10)
Number of blue marbles = (1/3) * 63 = 21
Number of green marbles = 27
Total number of marbles = red + blue + green = 10 + 21 + 27 = 58
Therefore, there are 58 marbles in total.
To determine the total number of marbles, we need to find the fraction representing the green marbles and then use that fraction to calculate the total number of marbles.
Given that 3/7 of the remainder after removing the red and blue marbles are green, we can set up an equation using algebra. Let's denote the total number of marbles as "x."
The fraction representing the green marbles is 3/7 of the remaining marbles after removing the red and blue marbles, which is (1 - 1/6 - 1/3) of "x." Simplifying this expression:
(1 - 1/6 - 1/3)x = 27
To solve the equation, let's first simplify the left side:
(6/6 - 1/6 - 2/6)x = 27
(3/6)x = 27
(1/2)x = 27
Now we can solve for "x" by multiplying both sides of the equation by 2:
x = 27 * 2
x = 54
Therefore, there are a total of 54 marbles in the box.