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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

Let x = number of 1-bedroom apartments y = number of 2-bedroom apartments z = number of 3-bedroom apartments

2. 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

3. jim_thompson5910

The number of 1-bedroom apartmenst is twice the number of 2-bedroom apartments means x = 2y

4. jim_thompson5910

An apartment complex contains 230 apartments each having 1, 2 or 3 bedrooms so x+y+z = 230

5. jim_thompson5910

you have this system of equations $\Large \begin{cases}y = 3z + 10\\x = 2y\\x+y+z = 230\end{cases}$

6. jim_thompson5910

Do you see how to solve?

7. anonymous

Honestly i dont...

8. anonymous

Its the only one i cant seem to get

9. 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

10. 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

11. jim_thompson5910

now solve 6z+20+3z+10+z = 230 for z

12. anonymous

omg thanks brother You helped me out a lot today

13. jim_thompson5910

no problem

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