anonymous
  • anonymous
An apartment complex contains 230 apartments each having 1, 2 or 3 bedrooms. The number of 2-bedroom apartments is 10 more than 3 times the number of 3-bedroom apartments. The number of 1-bedroom apartmenst is twice the number of 2-bedroom apartments. How many apartments of each kind are in the complex? Please answer with procedure
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
Let x = number of 1-bedroom apartments y = number of 2-bedroom apartments z = number of 3-bedroom apartments
jim_thompson5910
  • jim_thompson5910
`The number of 2-bedroom apartments is 10 more than 3 times the number of 3-bedroom apartments` gives the equation y = 3z + 10
jim_thompson5910
  • jim_thompson5910
`The number of 1-bedroom apartmenst is twice the number of 2-bedroom apartments` means x = 2y

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jim_thompson5910
  • jim_thompson5910
`An apartment complex contains 230 apartments each having 1, 2 or 3 bedrooms` so x+y+z = 230
jim_thompson5910
  • jim_thompson5910
you have this system of equations \[\Large \begin{cases}y = 3z + 10\\x = 2y\\x+y+z = 230\end{cases}\]
jim_thompson5910
  • jim_thompson5910
Do you see how to solve?
anonymous
  • anonymous
Honestly i dont...
anonymous
  • anonymous
Its the only one i cant seem to get
jim_thompson5910
  • jim_thompson5910
since y = 3z+10, we can replace the y in x = 2y with 3z+10 x = 2y x = 2*(3z+10) ... replace y with 3z+10 x = 6z+20
jim_thompson5910
  • jim_thompson5910
x+y+z = 230 6z+20+y+z = 230 ... replace x with 6z+20 6z+20+3z+10+z = 230 ... replace y with 3z+10
jim_thompson5910
  • jim_thompson5910
now solve `6z+20+3z+10+z = 230` for z
anonymous
  • anonymous
omg thanks brother You helped me out a lot today
jim_thompson5910
  • jim_thompson5910
no problem

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