Given:
Amount invested in fund A = $4000 less than investment in fund B.
Interest in fund A = 7% = 0.07
Interest in fund B = 5% = 0.05
Total profit = $1040
Let's find the amount invested in fund B.
For the investment in fund A, we have:
A = B - 4000
The equation below represents this total profit:
0.07A + 0.05B = 1040
Now, we have the system of equations:
A = B - 4000
0.07A + 0.05B = 1040
Where A is the amount invested in fund A while B is the amount invested in fund B.
Let's solve the system simultaneously using substitution method.
Substitute (B - 4000) for A in equation 2.
[tex]0.07(B-4000)+0.05B=1040[/tex]Apply distributive property:
[tex]\begin{gathered} 0.07B+0.07(-4000)+0.05B=1040 \\ \\ 0.07B-280+0.05B=1040 \end{gathered}[/tex]Combine like terms:
[tex]\begin{gathered} 0.07B+0.05B-280=1040 \\ \\ 0.12B-280=1040 \\ \\ \text{ Add 280 to both sides:} \\ 0.12B-280+280=1040+280 \\ \\ 0.12B=1320 \end{gathered}[/tex]Divide both sides by 0.12:
[tex]\begin{gathered} \frac{0.12B}{0.12}=\frac{1320}{0.12} \\ \\ B=11000 \end{gathered}[/tex]Therefore, the amount invested in Fund B is $11,000
ANSWER:
$11,000
