Chapter 1.9, Problem 17P

To determine

To calculate:

The two annual interest rates if person earned $\$121$ more on the larger investments than the smaller:

Answer to Problem 17P

The annual interest rate for the larger investment is $0.085$ and small investment is $0.055$ .

Explanation of Solution

Given information:

The Part of $260$ km trip at $80$ km/h and rest at $100$ km/h

Calculation:

Let, the interest obtained path in smaller investment is $x$ . Thus, the interest the person got in the smaller interest is $x+0.03$ :

Use the formula of the earning:

  $E=I\times R\mathrm{...}\left(1\right)$

Where,

  $E$ : Earnings

  $I$ : invested money

  $R$ : Rate

For first part:

  $E=1200\cdot x$

For second part:

  $E=2200\left(x+0.03\right)$

The person earned $\$121$ more on the larger investment than on the smaller investment:

  $2200\left(x+0.03\right)-121=1200x$

Use the distributive property:

  $\begin{array}{l}2200x+66-121=1200x\\ 2200x-55=1200x\end{array}$

Add to $55$ both sides of the equation:

  $\begin{array}{l}2200x-55+55=1200x+55\\ 2200x=1200x+55\end{array}$

Then, subtract $1200x$ from both the sides:

  $\begin{array}{l}2200x-1200x=1200x-1200x+55\\ 1000x=55\end{array}$

Divide both the sides by $55$ to isolate the $x$ -term:

  $\begin{array}{l}\therefore \frac{1000x}{1000}=\frac{55}{1000}\\ \therefore x=0.055\end{array}$

The interest rate for the smaller investments is $0.055$ .

Put $0.055$ for $x$ in $x+0.03$ :

  $\begin{array}{l}\therefore x+0.03=0.055+0.03\\ \therefore x=0.085\end{array}$

The interest rate for the smaller investments is $0.085$ .

  $\begin{array}{l}1200\left(0.055\right)+2200\left(0.085\right)=253\\ 66+167=253\\ 253=253\end{array}$

The annual interest for the larger investment is $0.085$ and small investment is $0.055$ .