greig gave james 1/4 of his orange and sold 1/3 of the remainder. greig remained with 80. calculate how many greig had at the beginning
To solve this problem, let's break it down step by step:
Step 1: Greig gave James 1/4 of his orange.
Let's represent the number of oranges that Greig had initially as "x." Therefore, Greig gave James 1/4 of x, which is (1/4)x.
Step 2: Greig sold 1/3 of the remainder.
After giving James 1/4 of his orange, Greig has (3/4)x left. Greig then sells 1/3 of this remaining amount, which is (1/3)((3/4)x) = (1/4)x.
Step 3: Greig remained with 80.
The amount that Greig remained with after selling (1/3)((3/4)x) is given as 80.
So, we have the equation:
(3/4)x - (1/4)x = 80.
Simplifying this equation, we get:
(2/4)x = 80.
Further simplification gives:
(1/2)x = 80.
To find x, we need to solve for x by multiplying both sides of the equation by 2:
x = 80 * 2.
Therefore, the initial number of oranges Greig had is:
x = 160.
Greig had 160 oranges at the beginning.
1/4 + (1/3 * 3/4) = 1/2
1 - 1/2 = 1/2
1/2 x = 80 ... x = ?
Let's solve this problem step-by-step:
Step 1: Calculate the portion of the orange that Greig gave to James.
Greig gave James 1/4 (or 1 out of 4) of his orange.
Step 2: Calculate the remaining portion of the orange.
To find the remainder, we subtract the portion given to James from the original whole. So the remaining portion is 1 - 1/4 = 3/4.
Step 3: Calculate the portion of the orange that Greig sold.
Greig sold 1/3 (or 1 out of 3) of the remaining 3/4 of the orange.
Step 4: Calculate the remaining portion of the orange after selling.
To find the remainder after the sale, we subtract the portion sold from the remaining portion. So the remaining portion after selling is (3/4) - (1/3).
Step 5: Calculate the value of the remaining portion after selling.
We are told that the value of the remaining portion of the orange after selling is 80.
Thus, (3/4) - (1/3) = 80.
Step 6: Calculate the value of 1 whole orange.
To find the value of 1 whole orange, we multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 12.
12 * [(3/4) - (1/3)] = 12 * 80.
9 - 4 = 960.
5 = 960 - 9.
5 = 951.
Step 7: Calculate the initial quantity of oranges that Greig had.
Since 5 represents 3/4 of the orange, we can set up a proportion to find the whole quantity:
3/4 = 951/x, where x is the whole quantity.
Rearranging the equation, we get:
4 * 951 = 3x.
x = (4 * 951) / 3.
Step 8: Calculate the value of x.
x = (4 * 951) / 3 = 12704 / 3 ≈ 4234.67.
Therefore, Greig initially had approximately 4234.67 oranges.