RadhaKrishnan wrote:
A total of $60,000 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 $60,000 for that year was $4,080, what is the value of x?
(1) x = 3y/4
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
We are given that $60,000 was invested for 1 year. We are also given that part of the investment earned x percent simple annual interest and the rest earned y percent simple annual interest. We are also given that the total interest earned was $4,080. Let’s start by defining a variable.
b = the amount that earned x percent simple interest
Using variable b, we can also say:
60,000 – b = the amount that earned y percent simple annual interest
Since we know that the total interest earned was $4,080, we can create the following equation:
b(x/100) + (60,000 – b)(y/100) = 4,080
Note that in the equation above, we express "x percent" as x/100 and "y percent" as y/100 in the same way that we would express, say, 24 percent as 24/100.
Statement One Alone:
x = 3y/4
Although we have an equation with x and y, we still need a third equation to be able to determine the value of x because our equation from the given information has three variables. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
From our given information we know that b is the amount that earned interest at the rate of x percent per year and that 60,000 – b is the amount that earned interest at the rate of y percent per year. Thus, we can create the following equation:
b/(60,000 – b) = 3/2
Without a third equation, statement two alone is not sufficient to determine the value of x.
Statements One and Two Together:
From the given information and statements one and two we have the following 3 equations:
1) b(x/100) + (60,000 – b)(y/100) = 4,080
2) x = 3y/4
3) b/(60,000 – b) = 3/2
Since we have 3 independent equations with variables x, y, and b, we are able to determine the value of x.
Answer: C
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