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Last year, Boris had $30,000 to invest. He invested some of it in an account that paid simple 5% interest per year, and he invested the rest in an account that paid simple 8% interest per year. After one year, he received a total of $1710 in interest. How much did he invest in each account?

Respuesta :

Solution:

using percents (rather than fractions) on the left side of the following equation

so multiply the right side by 100 to compensate:

EQUATION 1

[tex]5\text{ a + 8 b = (}1710)(100)[/tex]

EQUATION 2:

[tex]a\text{ + b = 30000}[/tex]

Solving for b in the last equation, we obtain:

EQUATION 3:

[tex]b\text{ = 30000 -a}[/tex]

now, replacing this b in equation 1, we get:

[tex]5\text{ a + 8 (30000-a) = (}1710)(100)[/tex]

this is equivalent to:

[tex]5a\text{ + 240000- 8a = 171000}[/tex]

Putting the like terms together we obtain:

[tex]5a\text{ - 8a = 171000}-240000[/tex]

this is equivalent to:

[tex]-3a\text{ = -69000}[/tex]

or

[tex]a\text{ =}\frac{69000}{3}=23000[/tex]

now, replacing this value in equation 3, we get:

[tex]b\text{ = 30000 -a}=\text{ 30000-23000= 7000}[/tex]

thus, the correct answer is:

23000 at 5%

7000 at 8%

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