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?
1 Answer
Feb 1, 2018
Explanation:
- 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 -
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# -
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# -
Now, find the value of x using eq. 1.
#x+y=17,000#
#x=17,000-8,000#
#x=9,000# -
Finally, the amount each account invested are;
#x=$9,000.00#
#y=$8,000.00#
