It's the civil war and General Lee has a huge army. He split it into two parts keeping 1/3 under his command and giving 2/3 to his trusted general Stonewell Jackson (do not count generally or Jackson themselves in any calculations) General Lee fights a battle and lose 30% of his men General Jackson runs into a strong union army and loses 30% of his men. They rejoin and now have 805 men. How many did general Lee start with.
let Army be the original total
Lee lost=Army*1/3*.3
Jackson lost=Army*2/3*.3
those left= original - losses or
805=Army-Army*1/3*.3 - Army*2/3*.3
805=army(1-.1-.2)=army*.7
army=805/.7= ....
To solve this problem, let's start by finding out how many men General Jackson had initially.
Given that General Lee kept 1/3 of the army under his command and gave 2/3 of the army to General Jackson, we can set up the following equation:
(2/3) * X = Number of men under General Jackson's command
Now, General Jackson loses 30% of his men in battle, which means he retains 70% of his initial count. We can set up another equation to calculate this:
(70/100) * (2/3) * X = Number of men remaining under General Jackson's command
Now, let's focus on the combined count of both Generals Lee and Jackson. We know that after rejoining, they have a total of 805 men. Therefore, we can set up another equation:
(1/3) * X + (70/100) * (2/3) * X = 805
Now, let's simplify and solve for X:
(1/3) * X + (70/100) * (2/3) * X = 805
(1/3) * X + (7/10) * (2/3) * X = 805
(1/3) * X + (7/10) * (2/3) * X = 805
Let's find a common denominator for the fractions:
(10/30) * X + (14/30) * X = 805
Combining the terms:
(24/30) * X = 805
Now, let's isolate X by multiplying both sides of the equation by 30/24:
X = (805 * 30) / 24
X = 1006.25
Since we can't have a fraction of a person, we round down to the nearest whole number. Therefore, General Lee started with 1006 men.