Please these word problem. A box contained fruits such as apples, oranges and pears. 3/5 of the fruits were apples. 1/4 of the remaining fruits were oranges and the rest were pears. If there were 60 pears in the box, how many oranges were there?
3/5 apples , so 2/5 of box others
1/4 *2/5 = 2/10 of box oranges
so
apples + oranges = 3/5 + 2/10 = 8/10 of box
so 2/10 of box is pears
2/10 box = 60
so box = 300 fruits
oranges = 2/10 * 300 = 60
Let's break down the information given step-by-step:
Step 1: Start with the total number of fruits in the box.
Let's assume the total number of fruits in the box is "x."
Step 2: Determine the number of apples.
We know that 3/5 of the fruits were apples. So, the number of apples can be calculated as:
3/5 * x = (3/5)x
Step 3: Calculate the remaining fruits.
To find the remaining fruits, we need to subtract the number of apples from the total number of fruits:
Remaining fruits = x - (3/5)x
= (5/5)x - (3/5)x
= (2/5)x
Step 4: Calculate the number of oranges.
We are given that 1/4 of the remaining fruits were oranges.
So, the number of oranges can be calculated as:
1/4 * (2/5)x = (1/4) * (2/5) * x
= (1/10)x
Step 5: Set up and solve an equation for the number of pears.
We are given that there were 60 pears in the box. Therefore, we can set up the equation:
60 = (2/5)x
Step 6: Solve the equation for x (total number of fruits).
To isolate x, we can multiply both sides of the equation by 5/2:
(5/2) * 60 = x
x = 150
Step 7: Calculate the number of oranges.
Now that we have determined the total number of fruits (x = 150), we can calculate the number of oranges:
(1/10) * 150 = 15
Therefore, there were 15 oranges in the box.
To solve this word problem, we can break it down into steps.
Step 1: Determine the fraction of apples in the box.
We are told that 3/5 of the fruits were apples. This means that if we add the numerator and denominator (3 + 5), we get a total of 8 parts. To find the fraction representing apples, we divide the numerator (3) by the total parts (8).
Apples = 3/8
Step 2: Determine the fraction of fruits that were not apples.
Since 3/5 of the fruits were apples, the remaining fruits would be 2/5. This is obtained by subtracting the fraction of apples from 1.
Remaining fruits = 1 - 3/5
Remaining fruits = 5/5 - 3/5
Remaining fruits = 2/5
Step 3: Determine the fraction of oranges in the remaining fruits.
We are told that 1/4 of the remaining fruits were oranges. So we multiply the fraction of the remaining fruits (2/5) by 1/4 to find the fraction representing oranges.
Oranges = 2/5 * 1/4
Oranges = 2/20
Oranges = 1/10
Step 4: Determine the number of oranges.
We know that there were 60 pears in the box. So, the remaining fruits (which include oranges) are equal to 60 pears. Since pears represent 2/5 of the remaining fruits, we can set up a proportion to solve for the number of oranges.
(1/10) / (2/5) = x / 60
To solve this proportion, we can multiply the numerators and the denominators:
5 * x = 60 * 1
5x = 60
x = 60 / 5
x = 12
Therefore, there were 12 oranges in the box.