Rose Harrison and Clara Huizink Solutions for Exercise 20: Practice 6

You open a small business with an initial investment of $\mathrm{\$} 90000$. The weekly running costs for the business are $\mathrm{\$} 7800$. The weekly revenue (income) from your business is $\mathrm{\$} 8800$. Determine how long will it be before you break even (when your total profit matches the amount you have invested.)

Between $2000$ and $2010$, coal and petroleum production from the fuel producing countries can be modeled by the following system of equations, where $x=0$ represents the year $2005$ :

Coal production : $y=93.2 x+3100$

Petroleum production : $y=-29.1 x+2942$

Calculate the year in which production from both forms of fuel was equal.

A phone company has two weekly plans to choose from. Plan A charges an operating fee of $\$31.45$, plus $15.5$ cents per minute. Plan $\mathrm{B}$ charges an operating fee of $\$5.20$, plus $37$ cents per minute. Determine how you would decide on which plan would be best for you, and explain your reasoning.

You gave $\mathrm{\$} 4500$ to an investment broker, who put part of the money in a fund paying $2\%$ annual interest and the rest in a fund paying $5\%$ annual interest. At the end of the year you receive $\mathrm{\$} 210$ in interest. Determine how much of your initial investment was placed into each fund.

Your uncle Karl wants to loose some weight by burning extra calories each week $(2\mathrm{kg}=\mathrm{approx}. 3000 \mathrm{calories})$. He will do it by riding a bicycle, which burns $350$ calories an hour, and by walking, which burns $200$ calories an hour. If the uncle Karl has $10$ hours per week to devote to exercise, what combination of walking and cycling will allow him to achieve his goal of burning exactly $3000$ calories.