Final answer:
None of the provided options (A, B, C, or D) correctly derive a value for 'y' from the initial equation 10 (84) = 500, as all suggested manipulations result in values other than 500.
Step-by-step explanation:
The question is asking which equation can be used to find the value of y when given the initial equation 10 (84) = 500. Let's analyze the provided options one by one.
- Option A) 10 (8y) = 500 suggests replacing the number 84 with 8y in the equation, which is incorrect because 8y would not equal 84 unless y = 10.5, and we are not given any such information.
- Option B) 5 (84) = y changes the multiplier from 10 to 5 and sets the result equal to y. This would make y equal to 5 times 84, which is 420, and not the 500 we are looking for.
- Option C) 10 (40) = y sets y equal to 10 times 40, which is 400, again not 500 as we need.
- Option D) 10 (21) = y would make y equal to 210, which is also incorrect.
Upon closer inspection, none of the provided options correctly transforms the equation 10 (84) = 500 into a new equation that allows us to solve for y. Therefore, there seems to be a mistake in the options provided and none can be used to find the correct value of y in context to the original equation.