On a TV game show, a contestant makes $600 for every correct answer but loses $500 for every wrong answer. After answering 22 questions, Sarah broke even. How many questions did she answer correctly?

If x correct, then

600x - 500(22-x) = 0
1100x = 500*22
x = 10

Well, it seems like Sarah was playing a high-stakes game. Let's do some clown math!

Since Sarah broke even, we can assume that the total amount she won is equal to the total amount she lost. So let's break it down:

For each correct answer, she made $600. So the total amount she made for the correct answers is 600x, where x is the number of correct answers.

For each wrong answer, she lost $500. So the total amount she lost for the wrong answers is 500y, where y is the number of wrong answers.

Since she broke even, we can set up the equation:

600x = 500y

Now, we know that she answered a total of 22 questions. So x + y = 22.

To solve this clown equation, let's find the values of x and y. *squeak*

Start with the equation 600x = 500y. We can divide both sides by 100 to simplify:

6x = 5y

Now, let's try out some values for x and y that satisfy both equations. *honk honk*

Let's start with x = 10, since it's an even number and it's always nice to start with a smile.

If x = 10, then 6x = 60.

Now, let's see if this value satisfies the second equation:

x + y = 22

10 + y = 22
y = 12

So, if Sarah answered 10 questions correctly and 12 questions incorrectly, she would break even.

But hey, keep in mind that this is just clown math! The real answer might be different, so double-check my calculations! *confetti*

Let's assume that Sarah answered x questions correctly.

For each correct answer, she earns $600, so the total amount of money she earns from correct answers is 600x.

For each wrong answer, she loses $500, so the total amount of money she loses from wrong answers is 500(22 - x) since she answered a total of 22 questions.

Since Sarah broke even, the amount earned from correct answers must be equal to the amount lost from wrong answers.

So, we can set up the following equation:

600x = 500(22 - x)

Now let's solve for x:

600x = 500(22 - x)
600x = 500*22 - 500x
600x + 500x = 500*22
1100x = 500*22
x = (500*22) / 1100
x = 10

Therefore, Sarah answered 10 questions correctly.

To solve this problem, we'll let "x" represent the number of questions Sarah answered correctly.

Since Sarah makes $600 for every correct answer, she earned a total of 600x dollars for the correct answers.

On the other hand, Sarah loses $500 for every wrong answer, so for the incorrect answers, she lost 500(22 - x) dollars.

Since she broke even overall, the amount she earned and lost should be equal, so we can set up the following equation:

600x = 500(22 - x)

Now, let's solve for x:

600x = 500(22 - x)
600x = 11,000 - 500x
600x + 500x = 11,000
1,100x = 11,000
x = 11,000 / 1,100
x = 10

Therefore, Sarah answered 10 questions correctly.