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a person had 16,000 infested into accounts, one paying 8% simple interest and one pin 9% simple interest. how much was invested in each account if the interest after one year is 1,379

Respuesta :

We know that

• The principal is $16,000.

,

• The simple interest rates are 8% and 9%.

,

• The interest obtained is $1,379.

,

• The time is 1 year.

We can express the following

[tex]x+y=16,000[/tex]

We know that the total interest for one year is $1,379, so

[tex]0.08x+0.09y=1,379[/tex]

Let's solve the first equation for x

[tex]x=16,000-y[/tex]

Then, we combine the equations

[tex]\begin{gathered} 0.08x+0.09y=1,379 \\ 0.08(16,000-y)+0.09y=1,379 \\ 1,280-0.08y+0.09y=1,379 \\ 0.01y=1,379-1,280 \\ y=\frac{99}{0.01} \\ y=9,900 \end{gathered}[/tex]

Now, we find x

[tex]x=16,000-y=16,000-9,900=6,100[/tex]

Hence, the 8% account has an investment of $6,100 and $9,900 for the 9% account.

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