SOLUTION: Part of 8,000 was invested at 10% and the rest at 12%. If the annual income from these investments was 860.00 how much was invested at each rate. I need help with this one.Each ra

Question 260828: Part of 8,000 was invested at 10% and the rest at 12%. If the annual income from these investments was 860.00 how much was invested at each rate. I need help with this one.Each rate meaning 10% and 12 %
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
total invested is 8,000

let x be one part.
let y be the other part.

you have x + y = 8000 (equation 1)

total annual income is 860.000

x part is invested at 10%
y part is invested at 12%

you have .10*x + .12*y = 860 (equation 2)

you need to solve these 2 equations simultaneously.

solve for y in equation 1 to get y = 8000 - x

substitute for y in equation 2 to get .10*x + .12*(8000-x) = 860

solve for x in equation 2.

equation is:

.10*x + .12*(8000-x) = 860

simplify to get:

.10*x + .12*8000 - .12*x = 860

simplify to get:

-.02*x + 960 = 860

subtract 960 from both sides of this equation to get:

-.02*x = -100

divide both sides of this equation by -.02 to get:

x = 5000

that means y = 3000 because x + y = 8000.

you have x = 5000 and y = 3000.

substitute in equation 2 to get:

.10*5000 + .12*3000 = 860

simplify to get:

500 + 360 = 860 which is true confirming the values for x and y are good.

your answer is:

$5000 was invested at 10% and $3000 was invested at 12%.

RELATED QUESTIONS
Part of a $8, 000 inheritance was invested at 10% interest and the rest was in- vested at (answered by stanbon)

an investment club invested part of $10,000 at 9% annual interest and the rest at 8%. If... (answered by josmiceli)

Part of $6,000 was invested at 10% interest and the rest at 12%. If the annual income... (answered by greenestamps)

Part of $8,000 was invested at 10% interest and the rest at 12%. If the annual income... (answered by richwmiller)

Part of $8,000 was invested by an investment club at 10% interest and the rest at 12%. If (answered by addingup)

An investment club invested part of $10,000 at 4% annual interest and the rest at 8%.... (answered by checkley79)

a woman invested part of 10,000 at 8% annual interest and the rest a 9% interest. Her... (answered by ewatrrr)

Me. Rich invested $200,000, part at 8% and the rest at 20%. His annual income from the... (answered by mananth)

Part of $11,000 was invested by an investment club at 10% interest and the rest at 12%.... (answered by TimothyLamb)