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Exercise 1:

a) See diagram above right.

b) 0, because it is the distance between a city and itself. This distance is necessarily zero.

c) The sum of the “intermediate stages” (i.e. between two cities) must be less than the possible general stage which is 680km.

**Brest is not identified on the map, but is located west of Rennes, in Brittany.**

So Julia leaves Brest for Rennes and travels 245km, she still has enough to do (680-245)=435km with her tank. Then from Rennes she can go either to Paris, or to Bordeau, or turn around (which is not our interest). Two cases are interesting:

1st case: If Julia decides to go to Bordeaux from Rennes, she will have emptied her tank since there is just enough to cover 435km. And it will have made in one general stage the Brest-Rennes-Bordeau route

2nd case : If Julia decides to go to Paris from Rennes, there will be enough left to drive 435-360 =75km with her tank, which is not enough to reach a big city from Paris, the capital. She will have made the Brest-Rennes-Paris trip in one general stage without having completely emptied the tank of her car.

d)The distance of the trip Rennes-Paris-Strasbourg = distance (Rennes-Paris)+ distance (Paris-Strasbourg) = 360+448 = 808km

e) If on average the vehicle has a speed of 100km/h, to travel 808km, or about 800km, it will take 8 hours.

Exercise 2:

a. There are 42 external girls in the sixth grade.

b. There are 27 boys in the ninth grade who are half-boarders.

c. There are 128 half-board girls.

d. There are 177 external boys.

e. There are 152 students in fifth grade.

f. There are 622 students.

g. 47 + 42 = 89 students in the fourth grade.

h. 41+46=87 boys in sixth grade.

i. 177 + 166 = 343 external .

j . 166 + 128 = 294 girls.

## The answers to the exercises on proportionality in 6th grade.

After consulting the** answers to these exercises on statistics in 6th grade**, you can return to the **exercises in 6th grade**.

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