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Lamar invested his savings in two investment funds. The amount he invested in Fund A was $8000 less than the amount he invested in Fund B. Fund A returneda 2% profit and Fund B returned a 5% profit. How much did he invest in Fund B, if the total profit from the two funds together was $1030?

Sagot :

Lamar invested is savings in two funds

Let the investment in fund B be $x

The investment in fund A will be $(x - 8000)

Fund A returned 2% anf fund B returned 5% profit

ROI on fund A is 2% and ROI on fund B is 5%

Let the profit of fund A be a

Let the profit of fund B be b

The formula to find the return on investment (ROI) is

[tex]\text{ROI}=\frac{\text{Profit }}{Investment}\times100\text{\%}[/tex]

To find the profit for A, by substituting the

[tex]\begin{gathered} \text{ROI}=2\text{\%} \\ \text{Investment}=x-8000 \\ \text{Profit=a} \end{gathered}[/tex]

The profit of A is

[tex]\begin{gathered} 2=\frac{a}{x-8000}\times100 \\ \text{Crossmultiply} \\ 2(x-8000)=100a \\ \text{Divide both sides by 100} \\ a=\frac{2(x-8000)}{100} \\ a=\frac{x-8000}{50} \\ a=0.02x-160 \end{gathered}[/tex]

To find the profit for B, by substituting the

[tex]\begin{gathered} \text{ROI}=5\text{\%} \\ \text{Investment}=x \\ \text{Profit}=b \end{gathered}[/tex]

The profit of B is

[tex]\begin{gathered} 5=\frac{b}{x}\times100 \\ \text{Crossmultiply} \\ 5x=100b \\ \text{Divide both sides by 100} \\ \frac{5x}{100}=\frac{100b}{100} \\ b=0.05x \end{gathered}[/tex]

Sum of the total profit is

[tex]\begin{gathered} \text{Profit of A + Profit of B =\$1030} \\ a+b=1030 \end{gathered}[/tex]

Substitute for a and b into the above expression

[tex]\begin{gathered} (0.02x-160)+0.05x=1030 \\ 0.02x-160+0.05x=1030 \\ \text{Collect like terms} \\ 0.02x+0.05x=1030+160 \\ 0.07x=1190 \\ \text{Divide both sides by 0.07} \\ \frac{0.07x}{0.07}=\frac{1190}{0.07} \\ x=\text{\$17000} \end{gathered}[/tex]

Hence, the investment in fund B, x, is $17,000

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