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Complete the following word problems using systems of equations.
1. Astronauts traveling to the International Space Station have to be very careful about
weight (it takes about 9 lbs of rocket fuel to send 1 lb of stuff to the station). Each
astronaut can bring approximately 11 lbs of personal items (mementos and clothes)
with them into space. Each memento weighs about 0.1 lb, and each item of clothing
weighs about 0.5 lbs. If an astronaut wanted to bring 30 items with them, how many
mementos and pieces of clothing would they bring?

Respuesta :

Answer:

10 mementos and 20 items of clothing

Step-by-step explanation:

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Using the system of linear equations, the astronauts will bring 10 mementos and 20 clothings.

Let :

  • mementos = m
  • Clothing = c

  • m + c = 30 - - - - - - - - - (1)
  • 0.1m + 0.5c = 11 - - - - - (2)

From (1) :

  • m = 30 - c - - - - (3)

Put m = 30 - c in (2)

0.1(30 - c) + 0.5c = 11

3 - 0.1c + 0.5c = 11

Collect like terms :

0.4c = 11 - 3

0.4c = 8

c = 8/0.4

c = 20

From (3) :

m = 30 - c

m = 30 - 20

m = 10

Therefore, Astronaut will bring 10 mementos and 20 clothings.

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