From the fridge, Mr Rafie took out 1/2 of his oranges and 1/3 of his apples. He then had a total of 360 oranges and apples in the fridge. Of the fruits he had taken out, he had 30 more oranges than apples left after selling 150 oranges and 60 apples. How many oranges did Mr Rafie have at first?
number of apples --- x
number of oranges --- 360-x
took out:
apples = x/3
oranges = (360-x)/2 = 180 - x/2
after selling 150 oranges, he had left (30 - x/2)
after selling 60 appes, he had left (x/3 - 60)
He now has 30 more apples than oranges:
(x/3 - 60) - (30 - x/2) = 30
x/3 + x/2 - 90 = 30
5/6 x = 120
x = 144
so at the start he had 144 apples and 360-144 or 216 oranges
check my arithmetic
Why did Mr. Rafie take half of his oranges and a third of his apples? Did he suspect they were plotting a fruity rebellion? ๐๐ As an expert in hilarious math, let's solve this juicy puzzle!
Let's assume Mr. Rafie had 'x' oranges at first. After taking out half, he had x/2 oranges left. Similarly, let's assume he had 'y' apples initially. After taking out one-third, he was left with 2y/3 apples.
According to the information, the total number of oranges and apples he had was 360:
x/2 + 2y/3 = 360
Now, we also know that he had 30 more oranges than apples after selling 150 oranges and 60 apples. So,
(x/2 - 150) = (2y/3 - 60) + 30
Simplifying,
x/2 - 150 = 2y/3 - 30
Now, let's solve these two equations and find the values of 'x' and 'y'!
Note: Apologies for the seriousness. Sometimes math problems can't be solved with just humor.
Let's assign variables to the unknowns in the problem.
Let:
x = total number of oranges Mr. Rafie had initially
y = total number of apples Mr. Rafie had initially
Given:
Mr. Rafie took out 1/2 of his oranges and 1/3 of his apples.
This means he has (1/2)x oranges remaining in the fridge.
This also means he has (2/3)y apples remaining in the fridge.
It is given that there are a total of 360 oranges and apples in the fridge:
(1/2)x + (2/3)y = 360 ...........(Equation 1)
It is given that after selling 150 oranges and 60 apples, Mr. Rafie had 30 more oranges than apples remaining:
(1/2)x - 150 = (2/3)y - 60 + 30
(1/2)x - (2/3)y = -120 ...........(Equation 2)
We now have a system of equations with equation 1 and equation 2.
Let's now solve this system of equations using substitution method:
From equation 1, we get:
(1/2)x = 360 - (2/3)y
x = (720 - 4y)/3 ...........(Equation 3)
Substitute the value of x from Equation 3 into Equation 2:
(1/2)((720 - 4y)/3) - (2/3)y = -120
(720 - 4y)/6 - (2/3)y = -120
(720 - 4y) - 4y = -720
720 - 8y = -720
8y = 1440
y = 1440/8
y = 180
Substitute the value of y = 180 into Equation 3 to get x:
x = (720 - 4(180))/3
x = (720 - 720)/3
x = 0
Therefore, Mr. Rafie initially had 0 oranges.
To solve this problem, let's break it down into steps:
Step 1: Determine the number of oranges and apples Mr. Rafie had initially
Let's assume Mr. Rafie had x oranges initially.
Then, Mr. Rafie also had x apples initially.
Step 2: Calculate the number of oranges and apples he took out from the fridge.
He took out 1/2 of his oranges, which is (1/2)x.
He also took out 1/3 of his apples, which is (1/3)x.
Step 3: Calculate the remaining number of oranges and apples.
After taking out the fruits, Mr. Rafie had x - (1/2)x = (1/2)x oranges left.
Similarly, he had x - (1/3)x = (2/3)x apples left.
Step 4: Calculate the total number of fruits (oranges and apples) after selling a portion.
According to the information, the total number of oranges and apples after selling a portion is 360.
So, we have the equation:
(1/2)x + (2/3)x = 360
Step 5: Solve the equation to find x (the initial number of oranges).
To solve the equation, we can multiply each term by 6 to eliminate the fractions:
3x + 4x = 360 * 6
7x = 2160
Dividing both sides of the equation by 7, we find:
x = 2160 / 7
x โ 308.57
Step 6: Calculate the initial number of oranges.
Since we assumed x oranges initially, Mr. Rafie initially had approximately 308.57 oranges.
Therefore, Mr. Rafie initially had approximately 308.57 oranges.