Question

Part of $3000 is invested at 12%, another part at 13%, and the remainder at 14%. The total yearly income from the three investments is $400. The sum of the amounts invested at 12% and 13% equals the amount invested at 14%. Determine how much is invested at each rate.

Answer 1

Lets start picking some variables here. We have three unknowns. Let use x , y and z.

Let x = amount invested at 12%
Let y = amount invested at 13%
Let z = amount invested at 14%

We know the total amount invested is
x + y + z = 3000

Each investment took a portion of that money so they sum up to 3000.

And the other equation is x + y = z. This comes from the fact that we were told that 12% and 13% invested equals the sum of 14% invested.

We know the total amount invested is 400 and that comes from all three investments.
0.12x + 0.13y + 0.14z = 400

So now you have three equations that can be used to find three unknowns.

Answer 2

So lets label equation
a.) x + y + z = 3000
b.) x + y = z
c.) 0.12x + 0.13y + 0.14z = 400

If you take equation b and plug it into equation a you get the following

2z = 3000

Now we can find what z is. Solve for z
z = 1500

Now we need to find x and y.

Since we know z we have equation a as

x + y + 1500 = 3000

x + y = 1500
Solve for y ---->>>> y = 1500 - x

Now plug this into equation c.)

0.12x + 0.13 (1500 -x) + 0.14 (1500) = 400

0.12x + 195 - 0.13x + 210 = 400
- 0.01x + 405 = 400
- 0.01x = -5

x = 500

Now we know both x and z. x = 500 and z = 1500

So find lets find y. Let's go back to equation a.) which is x + y + z = 3000.

Plug in x and z and solve for y.

500 + y + 1500 = 3000

y + 2000 = 3000
y = 1000

So we have all three variables found. x = 500, y = 1000 and z = 1500.

Answer 3

Why is this bumped? Wasn't is already solved?