An art teacher has a box of pencils. 1/10 are green, 1/2 are blue, 1/4 are orange, and the remaining 45 are red. How many pencils are orange?
1/10 + 1/2 + 1/4 = 31/40
So,
9/40 x = 45
x = 200
So, 1/4 * 200 = 50 are orange
To find out how many pencils are orange, we need to find the fraction that represents the orange pencils.
The fraction of pencils that are orange is 1/4 (as given in the problem statement).
Now, let's calculate the total number of pencils in the box by adding up the fractions of each color.
1/10 (green) + 1/2 (blue) + 1/4 (orange) + 45 (red pencils) = Total number of pencils
To add the fractions, we need to find a common denominator. The common denominator for 10, 2, and 4 is 20.
(2/20) + (10/20) + (5/20) + 45 = Total number of pencils
Simplifying the fractions:
(2/20) + (10/20) + (5/20) + 45 = Total number of pencils
1/10 + 1/2 + 1/4 + 45 = Total number of pencils
Multiplying each fraction by 20/20 (to give each fraction a common denominator):
2/20 + 10/20 + 5/20 + 45 = Total number of pencils
Adding the fractions:
(2 + 10 + 5)/20 + 45 = Total number of pencils
17/20 + 45 = Total number of pencils
Now, we can add the fractions:
17/20 + 45 = Total number of pencils
Converting the mixed number into an improper fraction:
(17/20) + (900/20) = Total number of pencils
Adding the fractions:
(17 + 900)/20 = Total number of pencils
917/20 = Total number of pencils
The total number of pencils in the box is 917.
Since we are looking for the number of orange pencils, we can multiply the total number of pencils (917) by the fraction representing the orange pencils (1/4):
917 * 1/4 = Number of orange pencils
The number of orange pencils is 229.
To find the number of orange pencils, we need to determine what fraction of the total number of pencils represents the orange pencils.
Let's start by calculating the fraction of each color:
The fraction of green pencils is given as 1/10.
The fraction of blue pencils is given as 1/2.
The fraction of orange pencils is given as 1/4.
The fraction of red pencils, which is not explicitly mentioned but can be determined using the given information, is given as the remaining 45 out of a total number of pencils.
To calculate the fraction of red pencils, we need to find the fraction that represents the red pencils out of the total number of pencils. We can subtract the fractions of the other colors from 1, since the total fraction should be equal to 1 (since it represents the whole).
The fraction of red pencils can be calculated as:
1 - (1/10 + 1/2 + 1/4)
Now, let's simplify the expression:
1 - (2/20 + 10/20 + 5/20)
1 - (17/20)
Now, we have the fraction of red pencils as 3/20.
Since the remaining 45 pencils represent this fraction of 3/20, we can set up a proportion to find the total number of pencils.
3/20 = 45/x
To solve for x, cross multiply and then divide:
3x = 20 * 45
3x = 900
x = 900 / 3
x = 300
Therefore, the total number of pencils is 300.
Since the question asks how many pencils are orange, and we previously found that the fraction of orange pencils is 1/4, we can calculate the number of orange pencils by multiplying the total number of pencils by this fraction:
Orange pencils = 300 * 1/4
Orange pencils = 75
Therefore, there are 75 orange pencils in the box.