Problem Solving

mitzwillrockgmat 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.

Can someone please explain how C is the answer.

I was able to break down the question as follows:

P is the amount invested @ x% while, (60,000-p) is the amt invested at y%

together they earn 4080;



px/100 + (60000-p)y/100 = 4080
px + (60000-p)y = 408,000


stat 1) given x=3y/4 we can substitute it to find y but we get stuck with P left to calculate . So insuff.

stat 2) (px/100) / (60000-p)y/100 = 3/2 . with this also one cant find x. so insuff.

But together I just dont see how they can solve x. there are 3 variables x , y & p while only two equations.

pls give me a break down of the calculation. thanks!
[/b]

clock60 wrote:

mitzwillrockgmat 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.

Can someone please explain how C is the answer.

I was able to break down the question as follows:

P is the amount invested @ x% while, (60,000-p) is the amt invested at y%

together they earn 4080;



px/100 + (60000-p)y/100 = 4080
px + (60000-p)y = 408,000


stat 1) given x=3y/4 we can substitute it to find y but we get stuck with P left to calculate . So insuff.

stat 2) (px/100) / (60000-p)y/100 = 3/2 . with this also one cant find x. so insuff.

But together I just dont see how they can solve x. there are 3 variables x , y & p while only two equations.

pls give me a break down of the calculation. thanks!
[/b]

hi friend
it is better to put DS question in proper section
as for the question, your reasoning in my humble opinion is valid but you stop half-way
(px/100) / (60000-p)y/100 = 3/2
px*100/(100y(60000-p)=3/2
cancel 100
px/(y(60000-p)=3/2
x/y=3*(60000-p)/2p
and from the 1st we are given that x/y=3/4
3*(60000-p)/2p=3/4
cancel 3, and 2
3p=120000
p=40000

and now we have 2 equations with 2 unknowns
x/y=3/4
40x+20y=4080
and now it is possible to calculate x
so C is valid answer