There is a box and inside it is a bunch of hats. 1/6 of the hats are red, 1/3 of the hats are blue. 3/7 of the remainder are green. There are 27 green hats. How many hats are there in total?
1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2
so half are red or blue, leaving half
3/7 * 1/2 = 3/14 are green
so
(3/14) x = 27
I think you can find x now. 9*14
To find the total number of hats, we will work step-by-step.
First, let's find the number of green hats in the box:
We are given that 3/7 of the remainder after removing red and blue hats are green, and we know that there are a total of 27 green hats. So, let's identify the remainder:
Let R be the total number of hats, then the remainder after removing red and blue hats is R - (1/6)R - (1/3)R = R(1 - 1/6 - 1/3) = R - R/6 - R/3 = R - (1/6 + 1/3)R = R - (1/6)R - (2/6)R = R - (1/2)R = (1/2)R.
And we are given that (3/7) of this remainder is equal to 27 green hats. So we can write an equation:
(3/7)(1/2)R = 27
(3/7)*(1/2)*R = 27
(3/14)*R = 27
Now, solving for R:
R = (27*14)/3
R = 126
Therefore, the total number of hats in the box is 126.