What does the solution x = 3 mean in the context of the situation?

Understand the Problem

The question is asking us to interpret the meaning of the solution to an equation related to a bat eating mosquitoes. Specifically, it requires understanding what the variable 'x' represents in the context of the problem and how it relates to the bat's consumption of mosquitoes.

Answer

It would take the bat 3 hours to eat 4,100 mosquitoes.

Steps to Solve

Understanding the equation context

The bat has already eaten 1,400 mosquitoes and needs to eat a total of 4,100 mosquitoes. The equation represents how many additional mosquitoes the bat needs to eat:

Total mosquitoes needed = Mosquitoes already eaten + Mosquitoes eaten per hour * Hours hunted.

This translates to the equation:

$$ 900x + 1,400 = 4,100 $$

Solving the equation

To find the value of $x$, we first isolate $x$ in the equation.

Subtract 1,400 from both sides:

$$ 900x = 4,100 - 1,400 $$

This simplifies to:

$$ 900x = 2,700 $$

Finding the value of x

Next, divide both sides by 900:

$$ x = \frac{2,700}{900} $$

This simplifies to:

$$ x = 3 $$

Interpreting the solution

Since $x = 3$, it represents the number of hours the bat would need to hunt and eat the additional mosquitoes required to reach a total of 4,100 mosquitoes.

The interpretation of the solution is that it would take the bat 3 hours to eat 4,100 mosquitoes.

More Information

This means that after having already consumed 1,400 mosquitoes, the bat will need 3 additional hours to consume the remaining mosquitoes to reach its goal of 4,100.

Tips

Confusing the amount of mosquitoes already eaten with the total needed; ensure to correctly interpret what the total quantity in the equation represents.
Misreading the value of $x$; it specifically pertains to the time needed to meet the goal, not the total number of mosquitoes.

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