Answer to Question #132991 in Algebra for Nhieu T Pham

Question

George’s consultancy firm has a large number of employees who use their own cars when
travelling to customers. The company pays 10¢ per kilometre travelled towards the cost of the
journey, plus an additional 25¢ for each visit made. Because many employees have complained
that this is not enough to cover the cost, George has decided to change the policy.
He can only afford to increase the total cost for an average week (40 visits covering a total of 300
kilometres) by 10%. The new policy will still offer a rate per kilometre, plus an amount per visit
(both of which will be a whole number of cents), and George wants the rate per kilometre to be as
high as possible.
What will be the amount paid for a visit involving travel of 20 kilometres?

Answer 1

Now  the total cost for an average week (40 visits covering a total of 300 kilometres) is

$$40\cdot0.25+0.1\cdot300=\$40$$

If George can only afford to increase the total cost for an average week by 10%, then the new total cost will be

$$40\cdot1.1=\$44$$

Let $x=$ the cost of one kilometre travelled in dollars. Then

$$x\cdot300\leq44$$

$$x\leq0.14$$

The amount paid for a visit involving travel of 20 kilometres will be

$$0.25+0.14\cdot20=\$3.05$$

The amount paid for a visit involving travel of 20 kilometres will be $3.05.