Question

Rajvir invests his summer earnings of $1343. He invests part of the money at 7%/year, and the rest at 11%/year. After 1 year, these investments earn $125.85 in simple interest. How much did he invest at each rate? (hint: interest earned = money invested × interest rate)

a. $600 at 7%, $743 at 11%
b. $743 at 7%, $600 at 11%
c. $800 at 7%, $543 at 11%
d. $543 at 7%, $800 at 11%

Answer 1

Rajvir invested $547 at 7% and $796 at 11%.

Step-by-step explanation:

Let's denote the amount of money Rajvir invested at 7% as 'x', and the amount he invested at 11% as 'y'.

According to the information given, the total amount Rajvir invested is $1343. Therefore, we can write the equation x + y = 1343.

Also, the interest earned from the 7% investment plus the interest earned from the 11% investment is $125.85. This can be expressed as 0.07x + 0.11y = 125.85.

We can now solve this system of linear equations to find the values of x and y.

Multiplying the first equation by 0.07 gives 0.07x + 0.07y = 94.01.

Subtracting this equation from the second equation gives 0.11y - 0.07y = 125.85 - 94.01.

Simplifying, we get 0.04y = 31.84.

Dividing both sides of the equation by 0.04, we find y = 796.

Substituting this value of y back into the first equation, we can solve for x. We get x + 796 = 1343. Solving for x, we find x = 547.

Therefore, Rajvir invested $547 at 7% and $796 at 11%.