Does anyone know how to set this up?

Question

Kelly has a total of $30,000 invested in 2 municipal bonds that yeild 8% and 10% respectivly. If the interest Kelly gets in a year from the bonds is $2640, how much does she have invested in each bond?

--this deals with matrices and linear equations. So its like x +y = #

Answer 1

let x equal the money you have in the bond at 8% and y equal the money you have in the bond at 10%
since you know the total amount of money you have invested is 30,000 you can state
1) x+y=30000
also, since you know the amount you earn in interest from the bonds is 2640 you can state
2) .08x + .1y = 2640
since you have two unknowns and two equations you can solve for the variables. if you solve equation 1 for x you find
x=30000 -y
you can then plug this into equation 2 to have
.08(30000-y) +.1y =2640
solving for y, you find y =12000
you can then plug this value for y into either equation 1 or 2 to solve for x
x=18000

Answer 2

Let x be the amount @ 8%, y the amount @ 10%. You get 2 equations:

x + y = 30,000
0.08 x + 0.10 y = 2640

Multiply the second equation by 100 to eliminate the decimals and the first by 8 to match coefficients with x. So

8x + 10y = 264,000
8x + 8y = 240,000

2y = 24,000
y = 12,000
x = 18,000

It's not hard enough to need matrices. A little practice, you can do these in your head.

Answer 3

Let the amount invested in the 8% bond be x
Then the amount invested in the 10% bond is y = 30,000 - x

Your equation is:

0.08 * x + 0.10 * (30,000 - x) = 2640

Solving, we get:

- 0.02 * x = - 360

x = 18,000

y = 30,000 - 18,000 = 12,000

So 18,000 is invested in the 8% bond, and 12,000 is invested in the 10% bond.

Answer 4

x*.08+(30000-x)*.1=2640
-.02x+3000=2640
-.02x=-360
x=18000 @ 8%
the other amount: 12000@10%