In a study of bat migration habits, 240 male bats and 160 female bats have been tagged. If 100 more female bats are tagged, how many more male bats must be tagged so that `3/5` of the total number of bats in the study are male?

Explanation

To solve the problem step by step, we will follow a systematic approach.

### Step 1: Understand the initial conditions
We have:
- Male bats = 240
- Female bats = 160

### Step 2: Calculate the new total of female bats after tagging more
If 100 more female bats are tagged:
- New total of female bats = 160 + 100 = 260

### Step 3: Define the total number of bats
Let \( x \) be the number of additional male bats that need to be tagged.
The total number of bats after tagging \( x \) more male bats will be:
- Total bats = Male bats + Female bats = \( 240 + x + 260 = 500 + x \)

### Step 4: Set up the equation for the ratio of male bats
According to the problem, \( \frac{3}{5} \) of the total number of bats must be male. Therefore, we can express this as:
- Male bats = \( 240 + x \)
- We need \( 240 + x = \frac{3}{5} \times (500 + x) \)

### Step 5: Solve the equation
Now we will solve the equation:
\[ 240 + x = \frac{3}{5} \times (500 + x) \]
Multiply both sides by 5 to eliminate the fraction:
\[ 5(240 + x) = 3(500 + x) \]
Expanding both sides:
\[ 1200 + 5x = 1500 + 3x \]
Now, isolate \( x \):
\[ 1200 + 5x - 3x = 1500 \]
\[ 2x = 1500 - 1200 \]
\[ 2x = 300 \]
\[ x = 150 \]

### Conclusion
Therefore, **150 more male bats must be tagged** so that \( \frac{3}{5} \) of the total number of bats in the study are male.

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