Question

Solve the equation: 89.7 = (7.8x) / (100 - x)

a) x = 2
b) x = 8
c) x = 10
d) x = 20

Answer 1

After attempting to solve the equation, the solution x = 92 was found, but this does not match any of the provided answer options. It appears there may be a typo in the question, or the correct answer is not listed among the options.

Step-by-step explanation:

To solve the equation: 89.7 = (7.8x) / (100 - x), we'll start by moving all terms involving x to one side and the constant to the other to setup a quadratic equation.

1. Multiply both sides by (100 - x) to get rid of the denominator: 89.7(100 - x) = 7.8x.
2. Distribute 89.7 into (100 - x): 8970 - 89.7x = 7.8x.
3. Combine like terms: 8970 = 97.5x.
4. Divide both sides by 97.5 to isolate x: x = 8970 / 97.5.
5. Complete the calculation: x = 92.

However, the solution x = 92 does not match any of the provided options (a) x = 2 (b) x = 8 (c) x = 10 (d) x = 20. Therefore, we must have made an error. Let's identify and correct the mistake.

1. Let's go back to the step of combining like terms: we should add 89.7x to both sides to get 89.7 + 7.8x on the right side giving us 89.7(100 - x) = 7.8x + 89.7x.
2. Combine the x terms: 8970 = 97.5x.

Since the mistake has been corrected, we can see that x = 92 is still the solution, but it is not an option in the multiple-choice answers.

Therefore, either there is a typo in the given answer choices, or the equation has no solution among the options provided. We need to double-check the original equation and ensure that we've correctly interpreted the problem.