SOLUTION: Alice's Restaurant has a total of 258 seats. The number of seats in the non-smoking section is 51 more than twice the number of seats in the smoking section. How many seats are in

Question 1010137: Alice's Restaurant has a total of 258 seats. The number of seats in the non-smoking section is 51 more than twice the number of seats in the smoking section. How many seats are in each section?
I have tried to solve this by doing this equation: x+y=258
2x+51=258
It seems that my equation does not work.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Your first equation is correct, but your second equation is not correct.

Let
x = number of seats in the non-smoking section
y = number of seats in the smoking section

"The number of seats in the non-smoking section is 51 more than twice the number of seats in the smoking section"
means that

(number of non-smoking seats) = 2*(smoking seats) + 51

(x) = 2*(y) + 51

x = 2y + 51

So the second equation should be x = 2y+51. Note: if you made x the number of seats in the smoking section, then you'd have y = 2x+51. It's the same idea, just with the variables swapped. You'll get the same answers either way.

-----------------------------------------------

Go back to x+y = 258 and replace x with 2y+51

x+y = 258
2y+51+y = 258

Now solve for y
2y+51+y = 258
3y+51 = 258
3y+51-51 = 258-51
3y = 207
3y/3 = 207/3
y = 69

Use this to find x
x = 2y+51
x = 2*69+51
x = 138+51
x = 189

There are 189 seats in the non-smoking section. There are 69 seats in the smoking section.
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