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anonymous

  • one year ago

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

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  1. jim_thompson5910
    • one year ago
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    Let x = number of 1-bedroom apartments y = number of 2-bedroom apartments z = number of 3-bedroom apartments

  2. jim_thompson5910
    • one year ago
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    `The number of 2-bedroom apartments is 10 more than 3 times the number of 3-bedroom apartments` gives the equation y = 3z + 10

  3. jim_thompson5910
    • one year ago
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    `The number of 1-bedroom apartmenst is twice the number of 2-bedroom apartments` means x = 2y

  4. jim_thompson5910
    • one year ago
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    `An apartment complex contains 230 apartments each having 1, 2 or 3 bedrooms` so x+y+z = 230

  5. jim_thompson5910
    • one year ago
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    you have this system of equations \[\Large \begin{cases}y = 3z + 10\\x = 2y\\x+y+z = 230\end{cases}\]

  6. jim_thompson5910
    • one year ago
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    Do you see how to solve?

  7. anonymous
    • one year ago
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    Honestly i dont...

  8. anonymous
    • one year ago
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    Its the only one i cant seem to get

  9. jim_thompson5910
    • one year ago
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    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

  10. jim_thompson5910
    • one year ago
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    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

  11. jim_thompson5910
    • one year ago
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    now solve `6z+20+3z+10+z = 230` for z

  12. anonymous
    • one year ago
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    omg thanks brother You helped me out a lot today

  13. jim_thompson5910
    • one year ago
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    no problem

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