Math Question... Word problem?

Question

A motel has 60 rooms with 2 or 3 beds inside. If the total of the beds in this motel is 140, and 8 of the 3-beds rooms are occupied, how many 3 beds rooms are still available there?


Help please, and show work...

Wow, thanks everyone. That really helped make sense of this problem.

^__^

Answer 1

Let x = number of rooms with 2 beds
let y = number of rooms with 3 beds

x + y = 60 (because that's how many rooms there are)
2x + 3y = 140 (because that's how many beds there are)

Multiply the first equation by - 2
-2x -2y = - 120
2x + 3y = 140

Add the columns.
y = 20, so x = 40

So there should be 12 rooms left with 3 beds.

Answer 2

Let x be the number of rooms with 2 beds
Let y be the number of rooms with 3 beds
Since there are only 60 rooms, x + y = 60
Since there are 140 beds: 2x + 3y = 140
You now have two equations for two unknowns.
Solve for x:
x + y = 60
x = 60 -y

ok now use the other equation, subsituting our new x in:
2x + 3y = 140
2( 60 - y ) + 3y = 140
120 - 2y + 3y = 140
120 + y = 140
y = 20
ok so we know y... now just go back to one of the equations and find x:

x = 60 -y
x = 60 - ( 20 )
x = 40

20 - 8 = 12 rooms that have 3 beds remain.

Answer 3

x + y = 60 (let x = 2 beds and y = 3 beds)
2x + 3y = 140

Solve for x and y

x + y = 60 (subtract x from both sides)
y = 60 -x

use the above equation and substitute into the second equation for y
2x + 3(60-x) = 140

2x + 180 - 3x = 140

-x + 180 = 140 (subtract 180 from both sides)

-x = -40 (divide both sides by -1)

x = 40
y = 60 -x

y = 60 -40
y = 20 (number of 3-bed rooms)

20 -8 = 12 3-bed rooms left.