Question

Alvin has $760 less invested in 7% than he has at 5%. If his annual income from these two investments is $51.20, how much does he have invested at each rate?

Answer 1

Alvin invested $110 at rate of 7% and invested $870 at rate of 5%

Explanation:

we know that

The simple interest formula is equal to

`I=P(rt)`

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem

Let

x------> the amount of money invested at rate of 5%

At rate of 7%

we have

`t=1\ years\\ P=(x-\$760)\\r=0.07`

At rate of 5%

we have

`t=1\ years\\ P=x\\r=0.05`

substitute in the formula

`51.20=(x-760)(0.07*1)+(x)(0.05*1)`

`51.20=0.07x-53.2+0.05x`

`51.20+53.2=0.12x`

`x=104.4/0.12=\$870`

therefore

Alvin invested ($870-$760)=$110 at rate of 7%

Alvin invested $870 at rate of 5%