SOLUTION: Barb has a total of $25,000 invested in two different accounts. One is a money market account paying 9.5% interest, while the other is a cd that pays 12% interest. She recieves $27

Question 68412This question is from textbook
: Barb has a total of $25,000 invested in two different accounts. One is a money market account paying 9.5% interest, while the other is a cd that pays 12% interest. She recieves $2700 in interest from these combined investments, after 1 year. How much does she have invested in each account? This question is from textbook

Found 2 solutions by checkley71, rmromero:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
.12x+.095(25000-x)=2700
.12x+2375-.095x=2700
.025x=2700-2375
.025x=325
x=325/.025
x=13000 amount invested @ 12%
25000-13000=12000 amount invested @ 9.5%
proof
.12*13000+.095*12000=2700
1560+1140=2700
2700=2700
---------------------
happy money-making :)
Answer by rmromero(383) (Show Source): You can put this solution on YOUR website!
I.What is Ask in the problem?
--> How much does she have invested in each account?

Given :
--> One money is a market account paying 9.5%
--> The other is a cd that pays 12% interest
--> Total money invested is $ 25,000
--> Barb receives $ 2,700 interest from these combined investments after a year

Representation:
Let x = the money invested in the market account that gets 9.5% interest
y = the money cd that pays 12% interest

Equations:
1. x + y = $ 25,000
2. 0.095x + 0.12y = $ 2,700

Solution:
A. Note: I can multiply the equation 2 by 1000 so that I won't deal with decimals.
95x + 120y = 2, 700,000

B. Write the two equation and solve.
x + y = $ 25, 000
95x + 120y = $ 2, 700, 000

C. Multiply -95 to x + y = $ 25,000 to eliminate x
-95x - 95y = -$ 2, 375, 000
95x + 120y = $ 2, 700, 000

D. Add the two equations
25y = $ 325, 000

E. Divide both sides by 25
y = $ 13, 000 money cd that pays 12% interest

F. Substitute $ 13, 000 to y to any of the two equation
x + y = $ 25, 000
x + $ 13, 000 = $ 25, 000
x = $ 12, 000 money invested in the market account with 9.5% interest
Checking:
1.
x + y = $ 25, 000
$ 13, 000 + $ 12, 000= $ 25, 000
$25, 000 = $ 25, 000 ---------> True
2. 0.95x + 0.12y = $ 2,700
$ 1, 140 + $ 1, 560= $ 2, 700
$ 2, 700 = $ 2, 700 ------------>True

Therefore the money invested in the market account is $ 12, 000 and the money cd is $ 13, 000.

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