Question

hi can you help me with this problem?Formulate a system of equations for the situation below and solve.Kelly Fisher invested a total of $20,000 invested in two municipal bonds that have yields of 7% (bond A) and 10% (bond B) interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1520, how much did she invest in each bond?bond A $ bond B $

Answer 1

Given:

• Total amount invested = $20,000

,

• Interest rate for Bond A = 7% ==> 0.07

,

• Interest rate for Bond B = 10% ==> 0.10

,

• Total interest = $1520

Let's find the amount she invested in each.

We have the equations:

• For Total amount invested:

A + B = 20000

• For Total interest earned:

0.07A + 0.10B = 1520

Hence, we have the system of equations:

A + B = 20000......................................equation 1

0.07A + 0.10B = 1520.........................equation 2

Where A and B represents the amount invested in each bond.

Let's solve the system using substiution method.

• Rewrite equation 1 for A:

Subtract B from both sides

A + B - B = 20000 - B

A = 20000 - B

• Substitute (20000 - B) for A in equation 2:

0.07(20000 - B) + 0.10B = 1520

0.07(20000) + 0.07(-B) + 0.10B = 1520

1400 - 0.07B + 0.10B = 1520

1400 + 0.03B = 1520

• Subtract 1400 from both sides:

1400 - 1400 + 0.03B = 1520 - 1400

0.03B = 120

• Divide both sides by 0.03:

`\begin{gathered} (0.03B)/(0.03)=(120)/(0.03) \\ \\ B=4000 \end{gathered}`

• Now, substitute 4000 for B in any of the equations:

A = 20000 - B

A = 20000 - 4000

A = 16000

Therefore, we have the solution:

A = 16000, B = 4000

Hence, we have:

• Amount invested in Bond A = , $16,000

,

• Amount invested in Bond B = , $4,000

ANSWER:

Bond A = $16,000

Bond B = $4,000