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,

$\frac{11}{100}(x)$

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

That is,

$\frac{13}{100}\lbrack5x+240)\rbrack$

Since, Betty receives $1344.48 in interest after one year

Therefore,

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

Hence, the investment at 11% is $1728.

The investment at 13% is,

$5(1728)+240=8880$

The investment at 13% is, $8880.