Matematika

A group of five friends have decided to make a trip to Egypt. In the travel agency we have been given a budget for seven days of 3650 € for the five.

1. After leaving the agency we commented that the price does not seem expensive and maybe there is a friend who signs up. But how much does the trip cost per person per day?

2. The agency has given us the following plane to calculate the distance from Luxor to Cairo. Calculate this distance and say what is the scale of the plane that the agency has given us.

3. On the 5th day we are going to visit the pyramids. The pyramid of Cheops has a length of 230m wide. The guide has forgotten how tall it is, so we have been thinking about how to calculate it. So we have made this scheme:

We know that the pole measures 2m, its shadow 2,24m and the shadow we can measure from the pyramid 38,28m. What is the current height of the pyramid? How much do we have to walk to surround it?

4. After calculating the height, we want to know what is its lateral area and its volume because the guide does not remember it.

5. The 6th day we will go to Cairo and as we have the day off we have decided to look at car rental prices. We want to rent 2 cars. Some tourists have told us that they paid 6350 EGP (Egyptian pounds) for 3 days to rent 3 cars. How much will it cost to rent two cars for two days?

6. In the car rental office they inform us that we have a surcharge of 5% for being under 25 years old but they apply a 3% discount for renting two cars. How much will we pay in euros? 20 EGP = 1 €

7. In the Museum of Pharaonic and Egyptian Art they tell us that 3 men took 8 days to build the pharaoh's sarcophagus. If this one died suddenly, they had to build it in 2 days. How many men were needed in this case?

8. On the 7th day we decided to go to the Khan El-Khalili bazaar to buy details for our families and after many laps we decided to buy the same details and bargain to get a good price. At the end we got 16 djellaba and 28 copies of papyrus at a total price of 232 €. Find out the price of each thing so that we can do accounts knowing that the djellaba cost twice as much as the papyri.

We have already taken the cars and we have thought of going to Alexandria. Gasoline costs 7.75EGP / l. How much does the round trip cost us if each car consumes 7 l/100km? If we leave Cairo at 08:15 am and to make the 2/5 of the journey, it takes 92min 40s, at what time will we arrive in Alexandria? Will we arrive in time to see the Library if they close at 1:30 p.m.?

10. In Alexandria lived Diophantus, a famous mathematician who was born around 210 AD. To know at what age he died, we hadto decipher his epitaph. Could you tell when he died and at what age?

It will be valued:

• The presentation of the work

• The development and correct procedure of the proposed problems

•The originality.

• The inclusion of at least two additional mathematical problems related to the topic and their corresponding answers.