Two Investments

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A total of $10,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $10,000 for that year was $285, what is the value of x?

(1)

(2) The ratio of the amount interest earned at the rate of x percent per year to the amount of interest earned at the rate of y percent per year was 8 to 11.

Review: Two Investments




Explanation

This question describes two distinct investments. If the principal of the first part is P, then we have dollars in interest from that investment and interest from the second investment. The sum of these two expression is 285, so . With a single equation and three variables, we are missing a pretty good amount of information at this stage. Let's turn to the data statements, examining them separately first, as always.

Statement (1) gives us a new equation, but we still have two equations and three variables. We could solve this for y and substitute into the equation we have, , but that would still leave us with a P that's not going away. This information is insufficient to find x.

Statement (2) gives us a ratio, it's saying the following:



As in the case of Statement (1) alone, we have two equations and three variables. Insufficient.

Combining the statements, we have three distinct equations and three variables, so we would be able to solve, if we took the time.

The correct answer is (C).


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