Three boys share some oranges .the first one gets 1/3of the total,the second one gets 2/3 if the remainder if the last boy has 12of the remains oranges how many were shared
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Define the total number of oranges and calculate the share for the first boy.
Let $T$ be the total number of oranges.
The first boy gets $\frac{1}{3}$ of the total oranges.
Oranges for the first boy $= \frac{1}{3} T$.
Step 2: Calculate the remaining oranges after the first boy's share.
Remaining oranges after the first boy $= T - \frac{1}{3} T = \frac{3}{3} T - \frac{1}{3} T = \frac{2}{3} T$.
Step 3: Calculate the share for the second boy.
The second boy gets $\frac{2}{3}$ of the remainder from Step 2.
Oranges for the second boy $= \frac{2}{3} \times \left(\frac{2}{3} T\right) = \frac{4}{9} T$.
Step 4: Calculate the remaining oranges after the second boy's share.
Remaining oranges after the second boy $= \frac{2}{3} T - \frac{4}{9} T$.
To subtract these fractions, find a common denominator, which is 9.
$\frac{2}{3} T = \frac{2 \times 3}{3 \times 3} T = \frac{6}{9} T$.
So, remaining oranges $= \frac{6}{9} T - \frac{4}{9} T = \frac{2}{9} T$.
Step 5: Use the information about the last boy's share to find the total number of oranges.
The last boy has 12 oranges, which is the final remainder calculated in Step 4.
$$ \frac{2}{9} T = 12 $$
To solve for $T$, multiply both sides by $\frac{9}{2}$:
$$ T = 12 \times \frac{9}{2} $$
$$ T = \frac{108}{2} $$
$$ T = 54 $$
The total number of oranges shared was 54.
The total number of oranges shared was $\boxed{\text{54}}$.
