question 2 of 13, step 1 of 1\njarvis invested some money at 12% interest. jarvis also invested $92 more…

question 2 of 13, step 1 of 1\njarvis invested some money at 12% interest. jarvis also invested $92 more than 2 times that amount at 7%. how much is invested at each rate if jarvis receives $1088.82 in interest after one year? (round to two decimal places if necessary.)\nanswer\nhow to enter your answer (opens in new window)\namount invested at 12%\namount invested at 7%\nkeyboard shortcuts\nkeypad
Answer
Explanation:
Step1: Let the amount invested at 7% be $x$.
The amount invested at 12% is $2x + 92$.
Step2: Set up the interest - equation.
The interest formula is $I=P\times r\times t$. Since $t = 1$ year, the total interest is the sum of the interest from the 7% investment and the 12% investment. So, $0.07x+0.12(2x + 92)=1088.82$.
Step3: Expand the equation.
$0.07x+0.24x+11.04 = 1088.82$.
Step4: Combine like - terms.
$(0.07x+0.24x)+11.04 = 1088.82$, which gives $0.31x+11.04 = 1088.82$.
Step5: Isolate the variable term.
Subtract 11.04 from both sides: $0.31x=1088.82 - 11.04=1077.78$.
Step6: Solve for $x$.
Divide both sides by 0.31: $x=\frac{1077.78}{0.31}=3476.71$.
The amount invested at 7% is $x = 3476.71$. The amount invested at 12% is $2x + 92=2\times3476.71+92=6953.42 + 92=7045.42$.
Answer:
amount invested at 7%: $$3476.71$ amount invested at 12%: $$7045.42$