Difficulty: Hard

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Thus R > 9000: total = 9000 + 3×9000 + (R - 9000) + 1×(R - 9000) = 36000 + 2(R - 9000). Set 36000 + 2(R - 9000) = 65000.

Simplify this expression and find the total when R is set such that the equation balances.

Rationale

R = 23500.

The equation simplifies as follows:

total = 9000 + 27000 + (R - 9000) + (R - 9000) = 36000 + 2(R - 9000).

Set this equal to 65000:

36000 + 2(R - 9000) = 65000.

Subtract 36000 from both sides:

2(R - 9000) = 29000.

Divide by 2:

R - 9000 = 14500.

Add 9000:

R = 23500.

A (65000) YOUR ANSWER

This is the total, not the value of R. Incorrect.

B (2(R - 9000) = 29000) YOUR ANSWER

This is an intermediate step, not the final answer.

C (29000) YOUR ANSWER

This is twice the difference, not R.

D (R - 9000 = 14500) YOUR ANSWER

This is another intermediate step.

E (14500) YOUR ANSWER

This is the difference (R - 9000), not R itself.

F (R = 23500) YOUR ANSWER

This matches the solved equation and is the correct answer.

G (23500) YOUR ANSWER

This gives the same numeric value but includes an extraneous note; the clean answer is R = 23500 as in choice F.

Conclusion

The equation resolves to R = 23500. All other choices either represent intermediate values or incorrect totals. Therefore, the correct answer is F.

Simplify this expression and find the total when R is set such that the equation balances.

R = 23500.

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