money/ investment equations

[purcherries]

You have $30,000 invested in 2 accounts. The savings account pays 5% annual interest while the checking account pays 2% per year. If the total interest for both accounts was $1,140, how much money is each account?

I tried;
.05x+.02x=1140
.07x=1140
x=16285.714
.05*16285.714=814.29
.02*16285.714=325.71

 

[masters]

You have $30,000 invested in 2 accounts. The savings account pays 5% annual interest while the checking account pays 2% per year. If the total interest for both accounts was $1,140, how much money is each account?

I tried;
.05x+.02x=1140
.07x=1140
x=16285.714
.05*16285.714=814.29
.02*16285.714=325.71

I believe I just answered this question. Surely, you didn't double post.

 

[wtn3210]

Questions worded this way are meant to be solved using 2 variables. The solution already listed implies that there is an equal amount of money invested in each account. furthermore, it is an incorrect solution because 16 285 in each account gives a total greater than 30000 + 1140 which is the total value at the end of one year. the correct answer is below.

Set up 2 equations with 2 variables.
x + y = 30000 and .05x + .02y = 1140
x = 30000 - y
using substitution, .05(30000 - y) + .02y = 1140
(.05 x 30000) - .05y + .02y = 1140
1500 - .03y = 1140
360 = .03y
12000 = y
thus, x + 12000 = 30000
x = 18000
The savings account (5% interest) started with $18000 and after one year has $18000 + $900 = $18900.
The checking account (2% interest) started with $12000 and after one year has $12000 + $240 = $12240.
Checking the work, 18900 + 12240 = 31140 = 30000 + 1140