formulate a system of equations for the situation below and solve. kelly fisher invested a total of $30,000…

formulate a system of equations for the situation below and solve. kelly fisher invested a total of $30,000 invested in two municipal bonds that have yields of 8% (bond a) and 9% (bond b) interest per year, respectively. if the interest kelly receives from the bonds in a year is $2580, how much did she invest in each bond? bond a $12000 bond b $18000

formulate a system of equations for the situation below and solve. kelly fisher invested a total of $30,000 invested in two municipal bonds that have yields of 8% (bond a) and 9% (bond b) interest per year, respectively. if the interest kelly receives from the bonds in a year is $2580, how much did she invest in each bond? bond a $12000 bond b $18000

Answer

Explanation:

Step1: Define variables

Let $x$ be the amount invested in bond A and $y$ be the amount invested in bond B. We know that the total amount invested is $30000$, so $x + y=30000$.

Step2: Set up interest - equation

The interest from bond A is $0.08x$ and from bond B is $0.09y$, and the total interest is $2580$. So $0.08x + 0.09y=2580$.

Step3: Solve the system

From $x + y=30000$, we get $x = 30000 - y$. Substitute $x = 30000 - y$ into $0.08x+0.09y = 2580$: $0.08(30000 - y)+0.09y=2580$. Expand: $2400-0.08y + 0.09y=2580$. Combine like - terms: $0.01y=2580 - 2400$. $0.01y = 180$. Solve for $y$: $y=\frac{180}{0.01}=18000$.

Step4: Find $x$

Substitute $y = 18000$ into $x = 30000 - y$, we get $x=30000 - 18000 = 12000$.

Answer:

bond A: $$12000$ bond B: $$18000$