Question

Fatuma invests a total of $26,500 in two accounts paying 10% and 14% annual interest, respectively. How much

was invested in each account if, after one year, the total interest was $3,150.00.
$_____was invested at 10% and
$_____was invested at 14%.

Answer 1

$14000 was invested at 10%

$12500 was invested at 14%

Explanation:

We'll need a system of equations to find the amounts invested at 10% and at 14%

• Let x represent the amount invested at 10% (10% = 0.1 interest rate)
• Let y represent the amount invested at 14% (14% = 0.14 interest rate)
• Let 0.1x represent the interest earned at 10%
• Let 0.14y represent the interest earned at 14%

First equation:

amount invested at 10% + amount invested at 14% = total amount invested.

Thus, our first equation is x + y = 26500

Second equation:

interest earned at 10% + interest earned at 14% = total interest earned

Thus, our second equation is 0.1x + 0.14y = 3150

Method to solve: We can solve using substitution by isolating x in the first equation. Then we must substitute the resulting equation for x in the second equation. This will allow us to first solve for y:

Step 1 (Isolating x in first equation):

(x + y = 26500) - y

x = -y + 26500

Step 2 (Plugging in x = -y + 26500 for x in 0.1x + 0.14y = 3150 to solve for y):

0.1(-y + 26500) + 0.14y = 3150

-0.1y + 2650 + 0.14y = 3150

0.04y + 2650 = 3150

0.04y = 500

y = $12500

Step 3: Now we can plug in 12500 for y in the second equation in our system to find x:

x + 12500 = 26500

x = $14000

Thus, the amount invested at 10% is $14000 while the amount invested at 14% is 12500

Optional Step 4: We can check that we've found the correct investment amounts by plugging in 14000 for x and 12500 for y in both equation in our system and checking that we get 26500 and 3150 respectively:

Checking solutions for first equation:

14000 + 12500 = 26500

26500 = 26500

Checking solutions for second equation:

0.1(14000) + 0.14(12500) = 3150

1400 + 1750 = 3150

3150 = 3150