last year, joe had $20,000 to invest. he invested some of it in an account that paid 10% simple interest per…

last year, joe had $20,000 to invest. he invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. after one year, he received a total of $1910 in interest. how much did he invest in each account? note that the aleks graphing calculator can be used to make computations easier. first account: $ second account: $

last year, joe had $20,000 to invest. he invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. after one year, he received a total of $1910 in interest. how much did he invest in each account? note that the aleks graphing calculator can be used to make computations easier. first account: $ second account: $

Answer

Explanation:

Step1: Let the amount invested in the 10% - interest account be $x$.

Then the amount invested in the 7% - interest account is $(20000 - x)$.

Step2: Calculate the interest from each account.

The interest from the 10% - interest account after one - year is $0.1x$, and the interest from the 7% - interest account after one - year is $0.07(20000 - x)$.

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

The total interest is $1910$, so $0.1x+0.07(20000 - x)=1910$.

Step4: Expand and simplify the equation.

$0.1x + 1400-0.07x=1910$. Combining like terms gives $0.1x-0.07x=1910 - 1400$, which simplifies to $0.03x=510$.

Step5: Solve for $x$.

Dividing both sides of the equation $0.03x = 510$ by $0.03$, we get $x=\frac{510}{0.03}=17000$.

Step6: Find the amount invested in the other account.

The amount invested in the 7% - interest account is $20000 - 17000 = 3000$.

Answer:

First account: $$17000$ Second account: $$3000$