jjjinapinch wrote:On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?
(1) The total amount of interest earned by Hannah's two investments in one year was $900.
(2) Hannah invested the $5,000 at 6 percent simple annual interest.
Official Guide question
Answer: E
We are given that Hannah invested $5,000 at x percent simple annual interest and invested another amount at y percent simple annual interest. We need to determine the amount that she invested at y percent simple annual interest. We can let this amount be n.
Statement One Alone:
The total amount of interest earned by Hannah's two investments in one year was $900.
Using statement one, we can set up the following equation:
5,000(x/100) + n(y/100) = 900
Multiplying the entire equation by 100, we have:
5,000x + ny = 90,000
Since we do not know the value of x or y, we cannot determine the value of n, and thus statement one alone is not sufficient to answer the question.
Statement Two Alone:
Hannah invested the $5,000 at 6 percent simple annual interest.
From statement two, we know that x is 6, and thus we can determine how much interest Hannah made from her investment at x percent interest.
5,000 x 6/100 = $300
However, we still do not know how much money was invested at y percent simple annual interest. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
From both statements, we have the following equation:
300 + n(y/100) = 900
Since we do not know the value of y, we still cannot determine a value for n.
Answer:
E
