# If pascal invests 4000 pesos at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5% of the total amount...

If pascal invests 4000 pesos at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5% of the total amount invested. (Use 2 variables) and check

rcmath | Certified Educator

Let x be amount invested at 5.5%, and y the total amount invested.

y=4,000+x

Let's construct the following table

Amount      4,000 Pesos              x pesos                y pesos
invested

Interest       4%                        5.5%                     4.5%
rate

Amount      `4/100*4000`             `5.5/100*x`                 `4.5/100*y`
of interest

If we add the amount of interest from the first two, we recieve the total amount, which is equal to the third column. Hence

`4/100*4000+5.5/100*x=4.5/100*y=>`

`160+0.055x=0.045y=>`

`160+0.055x=0.045(4000+x)=>`

`160+0.055x=180+0.045x=>`

`0.01x=20=>x=2000`

Hence 2,000 pesos should be invested at 5.5%

Check:

4000x4%=160

2000x5.5%=110

(4000+2000)x4.5%=270

160+110=270 correct