In a group of 30 soldiers have food enough for 40 days.how many soldiers should leave the group so that food is enough for 100 days? Find it
What is the answer.
To solve this problem, we need to understand the concept of proportionality.
Let's break down the information provided:
- There are 30 soldiers initially.
- The food is enough for 40 days for all 30 soldiers.
Now, we need to determine how many soldiers should leave the group so that the food can last for 100 days.
We can set up a proportion to solve for the unknown number of soldiers:
(Number of soldiers) / (Number of days) = Constant
Let "x" represent the number of soldiers leaving the group.
So, the new number of soldiers will be "30 - x."
Using the concept of proportionality, we can set up the following equation:
(30 - x) / 100 = 30 / 40
To solve for "x," we can cross-multiply and solve for "x":
(30 - x) × 40 = 30 × 100
Now, we can simplify the equation:
40(30 - x) = 3000
Expanding the equation:
1200 - 40x = 3000
Next, isolate the variable by subtracting 1200 from both sides:
-40x = 1800
Finally, divide both sides by -40 to find the value of "x":
x = -1800 / -40
x = 45
Therefore, to have enough food for 100 days, 45 soldiers should leave the group.
100/40 = 2.5 times as many days.
So, you want to have
30/2.5 soldiers.