If the battalion of soldiers is formed into a solid square,there would be sixteen fewer men in the front than there would be if they were formed into hollow square four deep. What is the required number of the soldiers.?
To find the required number of soldiers, we can break down the problem into smaller steps:
Step 1: Determine the number of soldiers in the front of the solid square.
Let's represent the number of soldiers in the front of the solid square as "x".
Step 2: Determine the number of soldiers in the front of the hollow square.
In a hollow square formation four deep, the number of soldiers in the front can be found by adding 16 to "x". So, the number of soldiers in the front of the hollow square is "x + 16".
Step 3: Calculate the total number of soldiers in the solid square.
Since a solid square has soldiers on all sides, the total number of soldiers in the solid square can be determined by multiplying the number of soldiers in the front by 4 (since there are four sides). So, the total number of soldiers in the solid square is 4 * x = 4x.
Step 4: Calculate the total number of soldiers in the hollow square.
Similar to the solid square, the total number of soldiers in the hollow square can be determined by multiplying the number of soldiers in the front (x + 16) by 4. So, the total number of soldiers in the hollow square is 4 * (x + 16) = 4x + 64.
Step 5: Set up the equation.
Since we want to find the number of soldiers, we can set up an equation based on the information from steps 3 and 4:
4x = 4x + 64
Step 6: Solve the equation.
By solving the equation, we find that "x" cancels out on both sides. This means that the equation has no solution. Therefore, there is no unique answer for the required number of soldiers. It seems that there is an error in the problem or additional information is missing.