Questions: Maria invests a total of 14,500 in two accounts paying 4% and 12% simple interest, respectively. How much was invested in each account if, after one year, the total interest was 1,340.00. A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use x as your variable to represent the amount of money invested in the account paying 4% simple interest. Equation: B) The answers are: was invested at 4% and was invested at 12%.

Maria invests a total of 14,500 in two accounts paying 4% and 12% simple interest, respectively. How much was invested in each account if, after one year, the total interest was 1,340.00.
A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use x as your variable to represent the amount of money invested in the account paying 4% simple interest.
Equation:
B) The answers are:
was invested at 4% and
was invested at 12%.

Transcript text: Maria invests a total of $\$ 14,500$ in two accounts paying $4 \%$ and $12 \%$ simple interest, respectively. How much was invested in each account if, after one year, the total interest was $\$ 1,340.00$. A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use $x$ as your variable to represent the amount of money invested in the account paying $4 \%$ simple interest. Equation: $\square$ B) The answers are: \$ $\square$ was invested at $4 \%$ and \$ $\square$ was invested at $12 \%$.

Solution

Solution Steps

To solve this problem, we need to set up a system of equations based on the information given. Let $ x $ be the amount invested at 4% interest. Then, the amount invested at 12% interest would be $ 14500 - x $. The total interest from both accounts after one year is $1340. We can set up the following equation for the total interest: $ 0.04x + 0.12(14500 - x) = 1340 $. Solving this equation will give us the value of $ x $, and subsequently, the amount invested at 12% can be found by subtracting $ x $ from $14500.

Step 1: Set Up the Equations

Let $ x $ be the amount invested at $ 4\% $ interest. Then, the amount invested at $ 12\% $ interest is $ 14500 - x $. The total interest earned from both accounts after one year is given by the equation: \[ 0.04x + 0.12(14500 - x) = 1340 \]

Step 2: Simplify the Equation

Expanding the equation, we have: \[ 0.04x + 1740 - 0.12x = 1340 \] Combining like terms results in: \[ -0.08x + 1740 = 1340 \]

Step 3: Solve for $ x $

Rearranging the equation gives: \[ -0.08x = 1340 - 1740 \] \[ -0.08x = -400 \] Dividing both sides by $-0.08$ yields: \[ x = 5000 \]

Step 4: Calculate the Amounts Invested

The amount invested at $ 4\% $ is: \[ 5000 \] The amount invested at $ 12\% $ is: \[ 14500 - 5000 = 9500 \]