kim won $53,000 on a slot machine in las vegas. she invested part at 2% simple interest and the rest at 3%…

kim won $53,000 on a slot machine in las vegas. she invested part at 2% simple interest and the rest at 3%. she earned a total of $1200 in interest. how much was invested at each rate? how much was invested at 2%? $ (simplify your answer.) how much was invested at 3%? $ (simplify your answer.)

kim won $53,000 on a slot machine in las vegas. she invested part at 2% simple interest and the rest at 3%. she earned a total of $1200 in interest. how much was invested at each rate? how much was invested at 2%? $ (simplify your answer.) how much was invested at 3%? $ (simplify your answer.)

Answer

Explanation:

Step1: Let the amount invested at 2% be $x$.

Then the amount invested at 3% is $(53000 - x)$.

Step2: Calculate the interest from each investment.

The interest from the 2% - investment is $I_1=0.02x$, and the interest from the 3% - investment is $I_2 = 0.03(53000 - x)$.

Step3: Set up the equation based on the total - interest.

The total interest is $1200$, so $0.02x+0.03(53000 - x)=1200$.

Step4: Expand and simplify the equation.

$0.02x + 1590-0.03x=1200$. Combining like terms gives $- 0.01x=1200 - 1590$. $-0.01x=-390$.

Step5: Solve for $x$.

Dividing both sides by $-0.01$, we get $x = 39000$.

Step6: Find the amount invested at 3%.

The amount invested at 3% is $53000 - x=53000 - 39000 = 14000$.

Answer:

How much was invested at 2%? $39000$ How much was invested at 3%? $14000$