If 9.59.5 plus 8.68.6 times a number equals the sum of the number and 83.583.5, what is the number? Express your answer as a simplified fraction or a decimal rounded to two places.
Question
If 9.59.5 plus 8.68.6 times a number equals the sum of the number and 83.583.5, what is the number? Express your answer as a simplified fraction or a decimal rounded to two places.
Solution
Let's denote the unknown number as x. The equation based on the problem is:
9.5 + 8.6x = x + 83.5
To solve for x, we first simplify the equation by subtracting x from both sides:
8.6x - x = 83.5 - 9.5
This simplifies to:
7.6x = 74
Next, we divide both sides by 7.6 to solve for x:
x = 74 / 7.6
Using a calculator, we find that x is approximately 9.74 when rounded to two decimal places.
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