SOLUTION: Hi Bottles P and Q are identical. Bottle P is 5/6 filled with water and Q is 3/4 filled with water. The ratio of the mass of P and its contents to the mass of Q and its contents i

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Question 1188337: Hi
Bottles P and Q are identical. Bottle P is 5/6 filled with water and Q is 3/4 filled with water. The ratio of the mass of P and its contents to the mass of Q and its contents is 12 to 11. Their total mass is 1150g. What is the mass of one empty bottle.
Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Bottles P and Q are identical.
Bottle P is 5/6 filled with water and Q is 3/4 filled with water.
The ratio of the mass of P and its contents to the mass of Q and its contents is 12 to 11.
Their total mass is 1150g.
What is the mass of one empty bottle.
:
let b = the mass of one empty bottle
let w = the mass of the water in a full bottle
:
"The ratio of the mass of P and its contents to the mass of Q and its contents is 12 to 11."
%28b%2B%285%2F6%29w%29%2F%28b%2B%283%2F4%29w%29 = 12%2F11
Cross multiply
11(b+(5/6)w) = 12(b+(3/4)w)
11b + (55/6)w = 12b + 3(3)w
11b + (55/6)w = 12b + 9w
Multiply by 6 get rid of the denominator
66b + 55w = 72b + 54w
55w - 54w = 72b - 66b
w = 6b
:
"Their total mass is 1150g."
2b + 5%2F6w + 3%2F4w = 1150
multiply by 12, get rid of the denominator
24b + 2(5)w + 3(3)w = 13800
24b + 10w + 9w = 13800
24b + 19w = 13800
Replace w with 6b from the 1st equation
24b + 19(6b) = 13800
24b + 114b = 13800
138b = 13800
b = 13800/138
b = 100 grams is the mass of the empty bottle
:
:
You can check this solution by substitution in the 2nd original equation
w=6b
w=6*100
2(100) + (5/6)600 + (3/4)600 =