The amount invested by Mr.Smith in 5% is $240 .
Step-by-step explanation:
We have , Mr. Smith invests a certain amount of money at 8% and twice as much at 5%. If his annual income from the two investments is $720 . Let us suppose that Mr.Smith invest $x so :
Amount of money invested in 5% is [tex]\frac{5x}{100}[/tex] . And, amount of money invested in 8% is twice that of 5% i.e. [tex]\frac{(2)5x}{100} = \frac{10x}{100}[/tex] .
Now, total investment is $720 so,
[tex]\frac{5x}{100}[/tex] +( [tex]\frac{(2)5x}{100} = \frac{10x}{100}[/tex] ) = $720
⇒ [tex]\frac{5x}{100} + \frac{10x}{100} = 720[/tex]
⇒ [tex]\frac{15x}{100} = 720[/tex]
⇒ [tex]\frac{100(720)}{15} = x[/tex]
⇒ [tex]x = 4800[/tex]
The amount invested by Mr.Smith in 5% is [tex]\frac{5x}{100}[/tex] i.e.[tex]\frac{5(4800)}{100} = 240[/tex]. ∴ The amount invested by Mr.Smith in 5% is $240 .
