 # You had $10,000 to invest. You put x dollars in a safe, gove Betsy Rhone 2021-12-21 Answered You had$10,000 to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression $0.05x+0.12\left(10,000-x\right)$.
a. Simplify the algebraic expression.
b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested $6000 in the safe, government-insured certificate of deposit. You can still ask an expert for help Expert Community at Your Service • Live experts 24/7 • Questions are typically answered in as fast as 30 minutes • Personalized clear answers Solve your problem for the price of one coffee • Available 24/7 • Math expert for every subject • Pay only if we can solve it ## Expert Answer hysgubwyri3 Answered 2021-12-22 Author has 43 answers Step 1 Given that we have to invest 10,000 and put x dollars in a self government -insured certificate that pays 5% and then invests rest of the money in corporate bonds that pays 12% interest. So the total interest earned at the end of the year is given by the function $0.05x+0.12\left(10000-x\right)$. We need to: 1) simplify the algebraic expression. 2) find the interest earned at the end of year if 6000 is invested in safe government insured certificate. Step 2 1) First let us simplify the expression. Let $y=0.05x+0.12\left(10,000-x\right)$ $y=0.05x+1200-0.12x$ $y=1200-0.07x$ is the simplified expression. Step 3 2) if 6000 invested in the safe government insured certificate of deposit. So $x=6000$. $y=1200-0.07\left(6000\right)$ $y=1200-420$ $y=780$. So the interest earned at the end of the year is 780. ###### Not exactly what you’re looking for? Hattie Schaeffer Answered 2021-12-23 Author has 37 answers Step 1 To determine the total interest earned at the end of the year if we invested 6000$ in the safe, government-insured certificate of deposit, we should use the simplification that we did in the answer of part (a) and we replace x by \$6000
Step 2
$1200-0.07x=1200-\left(0.07\cdot 6000\right)$
$=1200-420$
$=\mathrm{}780$
###### Not exactly what you’re looking for? nick1337

To simplify out the expression, we can distribute the multiplication over addition. (one of the properties)
$0.05x+1200-0.12x$
$=1200-0.07x$
We can use the equation we just determined to plug in 6000 for x to find the total interest.
$1200-0.07\cdot \left(6000\right)=780$