There are 18 astronauts that are trained to go to the space station. The space shuttle can hold 7 astronauts, and they do not want to launch a space shuttle
that is not full. If they want to send as man, astronauts as possible, how many
shuttles will launch, and how many of the astronauts will remain on Earth?
Number of space shuttles that are launched:
Astronauts still on Earth:

They would send 14 astronauts (two space shuttles) and the other  four astronauts will remain on Earth.

Step-by-step explanation:

18 divided into 7 would be 2 4/7... You would need three more astronauts to fill a third shuttle.

3/6   and 9/18

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4