Paul has $40000 to invest. his intent is to earn 9% interest on his investment. he can invest part of his money at 6% and part at 10% interest. how much does paul need to invest in each option to make a total of 9% return on his $40000 ?

Given

Paul has $40000 to invest &he can invest part of his money at 6% and part at 10% interest.

Find out  Paul  invest in each option to make a total of 9% return on  $40000 .

To proof

Paul invest = $ 40000

let us assume that x be the part of money he invested at 6%.

let us assume that (40000 - x) be the part of money he invested at 10 %.

6% written in the simpler form              

= 0.06

similarly,

10% written in the simpler form = 0 .1

9% written in the simpler form = 0.09

than the equation becomes

0.09 (40000) = (40000 - x ) 0.1 +  0.06x

3600 = 4000 - 0.1x + 0.06x

0.1x - 0.06x = 4000 - 3600

0.04x = 400

x = 10000

$ 10000 be the part of money he invested at 6%.

$30000 be the part of money he invested at 10 %.

Hence proved

a is the right answer