Alice puts money into two accounts, one with 2% annual interest and another with 3% annual interest. She invests 3 times as much in the higher yielding account as she does in the lower yielding account. If her total interest for the year is $27.50, how much did she invest in each account?

Question

Alice puts money into two accounts, one with 2% annual interest and another with 3% annual interest. She invests 3 times as much in the higher yielding account as she does in the lower yielding account. If her total interest for the year is $27.50, how much did she invest in each account?

Answer 1

amount invested at lower rate --- $x

amount invested at higher rate ---$ 3x

.02x + .03(3x) = 27.50
times 100
2x + 9y = 2750
11x = 2750
x = 250

so she invested $250 at 2%, and $750 at 3%

check:
.02(25) + .03(750) = 27.5

Answer 2

Let's assume Alice invested x dollars in the lower yielding account.

According to the given information, she invested 3 times that amount, 3x dollars, in the higher yielding account.

The interest earned from the lower yielding account can be calculated as 2% of x, which is (2/100)*x = 0.02x.

Similarly, the interest earned from the higher yielding account can be calculated as 3% of 3x, which is (3/100)*(3x) = 0.09x.

The total interest earned from both accounts is $27.50.

So, we can set up the equation:

0.02x + 0.09x = 27.50.

Combining like terms,

0.11x = 27.50.

Dividing both sides by 0.11, we find

x = 27.50/0.11 = $250.

Therefore, Alice invested $250 in the lower yielding account and 3 times that, $750, in the higher yielding account.

Answer 3

To solve this problem, we'll use algebraic equations.

Let's say Alice invests x dollars in the 2% annual interest account.
Since she invests 3 times as much in the higher yielding account, she invests 3x dollars in the 3% annual interest account.

The interest earned from the 2% account can be calculated as follows: 0.02 * x
The interest earned from the 3% account can be calculated as follows: 0.03 * (3x) = 0.09x

According to the problem, the total interest earned from both accounts is $27.50, so we can write the equation:

0.02x + 0.09x = 27.50

Combining like terms, we have:

0.11x = 27.50

Now, let's solve for x by dividing both sides of the equation by 0.11:

x = 27.50 / 0.11

x ≈ 250

So Alice invested approximately $250 in the 2% account.
Since she invested 3 times as much in the 3% account, she invested approximately $750 (3 * 250) in the 3% account.

Therefore, Alice invested $250 in the 2% account and $750 in the 3% account.