Gary works at Ghosts and Goblins, a Halloween store. He puts orange, black, and white Halloween candies in boxes. After he fills a box, 1/4 is orange, 1/6 is black, and 21 are white. How many candies does Boris put in each box?
1/4 +1/6 = 3/12 +2/12 = 5/12
12/12 - 5/12 = 7/12
so we finish filling 7/12 of the box with 21 white candles
if n is all the candles (7/12) n = 21
n = 12 * 21/7) = 12 * 3 = 36
3/12 + 2/12 = 5/12 amount in orange and black combined which leaves 7/12 as white
7/12 = 21/x : you know 21 is 7/12 of the total
x=36 : total number of candies
To find out how many candies Gary puts in each box, we need to add up the fractions representing the different colors of candies.
The fraction for orange candies is 1/4, the fraction for black candies is 1/6, and we are given that there are 21 white candies.
Let's add up these fractions to find the total fraction of candies in each box:
1/4 + 1/6 + 21/x = 1
To solve this equation, we first need to find a common denominator for 1/4 and 1/6. The least common multiple of 4 and 6 is 12.
Converting 1/4 and 1/6 to have a common denominator of 12:
(1/4) * (3/3) = 3/12
(1/6) * (2/2) = 2/12
Now our equation becomes:
3/12 + 2/12 + 21/x = 1
Adding the fractions:
5/12 + 21/x = 1
Subtracting 5/12 from both sides of the equation:
21/x = 1 - 5/12
Simplifying:
21/x = 12/12 - 5/12
21/x = 7/12
Now, we can cross multiply to solve for x:
7x = 21 * 12
7x = 252
Dividing both sides by 7:
x = 252/7
x = 36
Therefore, Gary puts 36 candies in each box.
To determine the number of candies Boris puts in each box, we need to find the total number of candies in one box.
Let's assign a variable for the total number of candies in one box, say "x".
Out of the total candies in the box:
- 1/4 is orange, which means there are (1/4)x orange candies.
- 1/6 is black, which means there are (1/6)x black candies.
- 21 are white candies.
The sum of these three types of candies gives us the total number of candies in the box:
(1/4)x + (1/6)x + 21 = x
To solve this equation, we can eliminate the fractions by multiplying both sides of the equation by the least common denominator (LCD) of 4 and 6, which is 12:
12 * [(1/4)x + (1/6)x + 21] = 12 * x
3x + 2x + 252 = 12x
5x + 252 = 12x
252 = 12x - 5x
252 = 7x
Now, we can solve for "x" by dividing both sides of the equation by 7:
252/7 = x
x = 36
Therefore, Boris puts 36 candies in each box at Ghosts and Goblins.