There are some hats 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 hats, how many hats are there all together?
1/6 + 1/3 = 1/2 red or blue
3/7 * 1/2 = 3/14 green
3/14 x = 27
x = 126
21 red
42 blue
27 green
How did you get those numbers?
Well, let's put on our thinking hats for this one! If 3/7 of the remaining hats are green, it means that the remaining 4/7 must equal 27 hats. So, let's do some hat-thematic calculations here. If 4/7 of the remaining hats are equal to 27, then 1/7 would be equal to 27/4. Now, if we multiply that by 7, we get 189/4. But since we can't have fractional hats, let's just round it up to 48.
So, if the remaining 4/7 of the hats are 48, that means the total number of hats in the box is 48 plus the 27 green hats we know about. That adds up to a grand total of 75 hats!
To find the total number of hats, we need to follow these steps:
Step 1: Determine the number of hats that are green.
We are given that 3/7 of the remainder (after accounting for red and blue hats) are green. Since we know there are 27 green hats, we can set up the equation:
3/7 * remainder = 27
Step 2: Solve for the remainder.
To find the remainder, we'll multiply both sides of the equation by 7/3:
remainder = (27 * 7/3) = 63
Step 3: Calculate the number of red hats.
Since 1/6 of the hats are red, we'll set up the equation:
1/6 * total hats = red hats
Step 4: Calculate the number of blue hats.
Since 1/3 of the hats are blue, we'll set up the equation:
1/3 * total hats = blue hats
Step 5: Calculate the total number of hats.
The total number of hats can be found by adding the number of red, blue, and green hats together:
total hats = red hats + blue hats + green hats
Now let's plug in the values we've found:
total hats = (1/6 * total hats) + (1/3 * total hats) + 63 + 27
To simplify this equation, we'll first find a common denominator for 1/6 and 1/3, which is 6:
total hats = (1/6 * total hats) + (2/6 * total hats) + 63 + 27
Totaling the fractions:
total hats = (3/6 * total hats) + 90
Now, we can multiply both sides of the equation by 6 to eliminate the fraction:
6 * total hats = 3 * total hats + 540
Simplifying this equation:
6 * total hats - 3 * total hats = 540
3 * total hats = 540
Finally, divide both sides of the equation by 3:
total hats = 540 / 3
total hats = 180
Therefore, there are 180 hats all together.
Super
Lily receives 30 messages on her cell phone. Of those messages, 1/5 are picture messages and 7/8 of the remainder are text messages. How many text messages does she receive?
1/6 + 1/3 = 1/2 red or blue
3/7 * 1/2 = 3/14 green
3/14 x = 27
x = 126
21 red
42 blue
27 green
DUH!!! >:)