Question

A man invests $17,000 in two accounts. One account earns 5% interest per. year and the other earns 6.5& interest per year. If his total interest after one year is $970.00, how much did he invest in each account?

Answer 1

`1st " account"=$8,000.00`
`2nd " account"=$9,000.00`

Explanation:

1. Assume variables for these two accounts;
   Let:
   x= the 1st account @ 5% per year
   y= the 2nd account @ 6.5% per year
   The other data provided in the problem are as follow:
   $17,000.00= the sum of the two accounts
   $970.00= the total interest of the two accounts

2. Formulate equations from these accounts as provided in the problem; i.e.,
   `x+y=17,000->eq.1`
   `0.05x+0.065y=970->eq.2`

3. Solve the equation simultaneously. Multiply the first equation by -0.05 to cancel the x variable to find the value of y as shown below.
   `x+y=17,000 color(red)}color(red)(-0.05`
   `ul(0.05x+0.065y=970)`
   `cancel(-0.05x)-0.05y=-850`
   `ul(cancel(0.05x)+0.065y=970)`
   `0.015y=120`
   `y=120/0.015`
   `y=8,000`

4. Now, find the value of x using eq. 1.
   `x+y=17,000`
   `x=17,000-8,000`
   `x=9,000`

5. Finally, the amount each account invested are;
   `x=$9,000.00`
   `y=$8,000.00`