• September 16th, 2008, 02:53 PM
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)
(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!
• September 16th, 2008, 04:47 PM
DrRocket
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)
• September 17th, 2008, 12:22 PM
rgba
Hey DrRocket,

Thanks very much for the help! Ah, well I did actually work it out that way, but I made a mistake with my signs, I was dividing by 0.02 when it should have been 0.08!

Cheers!