Question

Susan invested $10,000 in two accounts. If one account yields 4% interest and the other yields 6%, what is the amount invested at 4% and 6% respectively?

a) $4000 at 4%, $6000 at 6%
b) $6000 at 4%, $4000 at 6%
c) $5000 at 4%, $5000 at 6%
d) $3000 at 4%, $7000 at 6%

Answer 1

To find the amount invested at 4% and 6%, you can set up a system of equations using the given information. The amount invested at 4% is $6,000 and the amount invested at 6% is $4,000.

Step-by-step explanation:

To find the amount invested at 4% and 6%, we can set up a system of equations using the given information. Let x represent the amount invested at 4% and y represent the amount invested at 6%. Since Susan invested a total of $10,000, we have the equation x + y = 10,000. We also know that the interest from the first account at 4% should be equal to the interest from the second account at 6%. Using this information, we can set up another equation: 0.04x = 0.06y. Now we can solve the system of equations.

First, let's rearrange the second equation and solve for x:

0.04x = 0.06y
x = (0.06y) / 0.04
x = 1.5y

Substituting this value of x into the first equation:

1.5y + y = 10,000
2.5y = 10,000
y = 10,000 / 2.5
y = 4,000

Now we can substitute the value of y back into the equation x = 1.5y to find x:

x = 1.5 * 4,000
x = 6,000

Therefore, the amount invested at 4% is $6,000 and the amount invested at 6% is $4,000.