Greg give 1/4 of his oranges to James and sold 1/3 of the remainder. Greg remained with 80 oranges. Calculate how many oranges Greg had in the beginning and calculate how many oranges were sold.
after giveaway: greg has (2/3)x
after sale he has (2/3)(2/3)x = (4/9)x
(4/9)x=80
x = 180
take over
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Let's denote the number of oranges Greg had in the beginning as "x".
According to the given information, Greg gave 1/4 of his oranges to James, which means he had 3/4 of the oranges left: (3/4)x.
Then, Greg sold 1/3 of the remaining oranges. After the sale, he remained with 80 oranges. So, the equation becomes:
(2/3)(3/4)x = 80
Let's solve this equation to find the value of "x":
(2/3)(3/4)x = 80
(6/12)x = 80
(1/2)x = 80
Now, we can find the value of "x":
x = (80 * 2) / 1
x = 160
Therefore, Greg had 160 oranges in the beginning.
To calculate the number of oranges sold, we can subtract the remaining 80 oranges from the initial number of oranges:
Number of oranges sold = 160 - 80 = 80
Therefore, Greg sold 80 oranges.
To solve this problem, we need to work backwards starting with the final number of oranges.
Let's assume that the number of oranges Greg had in the beginning was x.
According to the problem, Greg gave 1/4 of his oranges to James. This means he gave away (1/4)x oranges.
The remainder can be calculated by subtracting the given fraction from the total number of oranges:
Remainder = x - (1/4)x
Next, Greg sold 1/3 of the remainder. This means he sold (1/3)(x - (1/4)x) oranges.
The remaining number of oranges after the sale is 80, so we can set up an equation:
Remainder - (1/3)(x - (1/4)x) = 80
Simplifying the equation, we have:
(3/4)x - (1/3)(3/4)x = 80
(3/4)x - (1/4)x = 80
(2/4)x = 80
x/2 = 80
Now, we can solve for x:
x = 80 * 2
x = 160
Therefore, Greg had 160 oranges in the beginning.
To calculate the number of oranges sold, we substitute the value of x back into the equation (1/3)(x - (1/4)x):
(1/3)(160 - (1/4)160)
Simplifying, we get:
(1/3)(160 - 40)
(1/3)(120)
40
Therefore, Greg sold 40 oranges.