Question

Betty invested some money at 11 % interest. Betty also invested $240 more than 5 times that amount at 13%. How much is investedat each rate if Betty receives $1344.48 in interest after one year? (Round to two decimal places if necessary.)Step 2 of 2: Solve the system of equations.

Answer 1

Given:

Let x be the principal.

Betty invested some money at 11 % interest.

That is,

`(11)/(100)(x)`

Betty also invested $240 more than 5 times that amount at 13%.

That is,

`(13)/(100)\lbrack5x+240)\rbrack`

Since, Betty receives $1344.48 in interest after one year

Therefore,

`\begin{gathered} (11)/(100)(x)+(13)/(100)\lbrack5x+240)\rbrack=1344.48 \\ (11x)/(100)+(65x)/(100)+(13(240))/(100)=1344.48 \\ (76x)/(100)+31.2=1344.48 \\ (76x)/(100)=1344.48-31.2 \\ (76x)/(100)=1313.28 \\ 76x=131328 \\ x=1728 \end{gathered}`

Hence, the investment at 11% is $1728.

The investment at 13% is,

`5(1728)+240=8880`

The investment at 13% is, $8880.