word problem, please help!

Hi,

I'm going over a book on elementary algebra and came across the following word problem:

**A sum of $2100 is invested, part of it at 3% interest and the remainder at 5%. If the interest earned by the 5% investment is $51 more than the interest earned by the 3% investment, find the amount invested at each rate.**

I tried to solve:

**interest = principal * rate * time**

interest = principal * rate (since time is assumed to be 1)

i = pr

**sum = 2100**

px = 2100 - py

py = ?

rx = 0.03

ry = 0.05

ix = iy - 51

iy = ix + 51

I assumed that the sums of interest parts is equal to the sums of parts and rates, as below:

**ix + iy = px(rx) + py(ry)**

(iy - 51) + (ix + 51) = (2100 - py)0.03 + 0.05py

ix + iy = 63 + 0.02py

I just can't solve this problem! Hope you can help out!

Thanks!

Re: word problem, please help!

Quote:

Originally Posted by **rgba**

Hi,

I'm going over a book on elementary algebra and came across the following word problem:

**A sum of $2100 is invested, part of it at 3% interest and the remainder at 5%. If the interest earned by the 5% investment is $51 more than the interest earned by the 3% investment, find the amount invested at each rate.**

I tried to solve:

**interest = principal * rate * time**

interest = principal * rate (since time is assumed to be 1)

i = pr

**sum = 2100**

px = 2100 - py

py = ?

rx = 0.03

ry = 0.05

ix = iy - 51

iy = ix + 51

I assumed that the sums of interest parts is equal to the sums of parts and rates, as below:

**ix + iy = px(rx) + py(ry)**

ix + iy = 63 + 0.02py

I just can't solve this problem! Hope you can help out!

Thanks!

You made this more complicated than it needs to be, but you were on the right track. That caused you make a mistake in the basic equation that need to be solved. Try

51 = + 0.05py - 0.03 (2100 - py)