Inhabiting the solar system
Humanity is spreading. People live in small cities on the Moon and Mars. Every settlement is inhabited by 460 astronauts. From Earth, more people are coming in spaceships, each fit 140 astronauts. At present, 8340 people live in space distributed in 23 places. These places can be cities and spaceships. How many settlements are there?
The answer is 16.
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1 solution
Every settlement is inhabited by 460 astronauts, every spaceship by 140 astronauts.
(I): 4 6 0 ( a s t r o n a u t s ) ⋅ x ( s e t t l e m e n t ) + 1 4 0 ( a s t r o n a u t s ) ⋅ y ( s p a c e s h i p ) = 8 3 4 0 ( a s t r o n a u t s )
(II): x + y = 2 3
(II): x = 2 3 − y
x in (I): 4 6 0 ⋅ ( 2 3 − y ) + 1 4 0 ⋅ y = 8 3 4 0
x in (I): 3 2 0 ⋅ y = 2 2 4 0
y = 7
y in (I): 4 6 0 ⋅ x + 1 4 0 ⋅ 7 = 8 3 4 0
x = 1 6
At Present, there are 7 spaceships (y) and 16 settlements (x) in space.