Prospectors are drilling for oil. The cost of drilling to a depth of 50 m is £500. To drill a further 50 m costs £640 and, hence, the total cost of drilling to a depth of 100 m is £1140. Each subsequent extra depth of 50 m costs £140 more to drill than the previous 50 m.

a. Show that the cost of drilling to a depth of 500 m is £11 300.

b. The total sum of money available for drilling is £76 000. Find, to the nearest 50 m, the greatest depth that can be drilled.