Question

Alice put $68,000 in two different accounts. One account pays 6.5% and the other 7% interest. If the total amount earned in one year is $4,535, how much did she invest in each account?

Answer 1

Just solve the system of equations in 2 variables.
.065x + .07y = 4535
x+y=68000

Answer 2

How do I solve the first equation?

Answer 3

It's a system of equations. You solve them together.

Answer 4

You solve them both at once. By substitution

Answer 5

.065x^2+.07y^2=72535???????????

Answer 6

No

Answer 7

did I do that correct?

Answer 8

Am I way off?

Answer 9

4535 * 7
4535 * 65???

Answer 10

68000+4535=72535?

Answer 11

.065x + .07y = 4535
x+y=68000

use the second equation, x+y=68000, to rearrange for y=, to get: y = 68000-x

Now, replace y in the first equation with that:
\[\Large .065x + .07(68000 - x) = 4535\]

Answer 12

.065x+476-.07x=4535??

Answer 13

if you meant... \[\Large .065x+4760-.07x=4535\]Then it looks good so far (you had a 476 not 4760). Now try solving that for x. It might help to first rearrange the order like so:
\[\Large .065x-.07x +4760 =4535\]

Answer 14

.06x-.07x=-225

Answer 15

how does that look?

Answer 16

Well.. close, but now you dropped another number...

\[\Large .065x-.07x=-225 \] Now just combine the x terms and find x.

Answer 17

add .07 to each side?
add .065 to each side?

Answer 18

No, combine like terms. For example, 2x + 3x = 5x, or 4x - 7x = -3x.

Combine the 0.065x-0.07x to get...?

Answer 19

.135

Answer 20

One is being subtracted from the other...

Answer 21

.005=-225

Answer 22

.005x=-225

Answer 23

0.065x - 0.07x doesn't equal 0.005x, but you're close... be careful with negatives.

Answer 24

-.005x=-225

Answer 25

Correct. Now find x.

Answer 26

=45000

Answer 27

x=45000

Answer 28

is 45000 6.5%??

Answer 29

.065x + .07y = 4535

yep, since it has the 0.065 in front.

Answer 30

23000 is 7%??

Answer 31

Yep.