Oct 2021 Challenge

1. 25 drag racers come to the track to determine the top 3 cars by speed.
   Unhappily all the timing mechanisms are broken, so the races must be determined, head-to-head. Now the track has 5 lanes, and so 5 cars can race at a time. The question is what is the minimum number of races to determine the top 3 drag racers?

Solution:

2. What is the distance from town A to town G, if town A is eleven miles north of town B, town B is eight miles east of town C, town D is seven miles south of town C, town E is five miles west of town D, town F is three miles north of town E and town F is seven miles east of town G?

Solution:

Distance between Towns A and G:

North to South miles = 11 + 7 – 3 = 15 and
East to West miles = 8 + 5 + 7 = 20

Thus, (A to G)² = (15)² + (20)² = 225 + 400 = 625

Therefore, the distance between Towns A and G = √625 = 25 miles

3. Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost £75 each, and tickets to sit on the lawn during the concert cost £40 each. Organizers of the concert announced that 350 tickets had been sold and that £19,250 had been raised through ticket sales alone. What number of tickets were sold for the concert’s bench seats (B), and for the lawn seats, (L)?

Solution:

Given: B + L = 350 or L = 350 – B or B = 350 – L

and: B (75) + L (40) = 19,250

Then, B (75) + (350 – B) (40) = 19,250

75B + 14,000 – 40B = 19,250

                              35B = 19,250 – 14,000 = 5,250

                                   B = 5,250 / 35 = 150 bench tickets sold and

                 L = 350 – B = 350 – 150 = 200 lawn tickets sold

4. A dress on sale in a shop is marked at £65. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay?

Solution:

Let x = staff member’s cost

Therefore, x = (£65 * 0.85) * 0.9 = £49.73