SOLUTION: Sally has a glass that is 1/3 filled with syrup. Bob has a glass that is 1/4 filled with syrup but Bob's glass holds twice as much as Sally's. If they were to fill the rest of th

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Question 471866: Sally has a glass that is 1/3 filled with syrup. Bob has a glass that is 1/4 filled with syrup but Bob's glass holds twice as much as Sally's. If they were to fill the rest of their glasses with milk, then mix them together, what part of the combine mixture would be syrup.
Please let me know the process of solving this problem.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Sally has a glass that is 1/3 filled with syrup.
Bob has a glass that is 1/4 filled with syrup but Bob's glass holds twice as much as Sally's.
If they were to fill the rest of their glasses with milk, then mix them together, what part of the combine mixture would be syrup.
:
let x = amt to fill Sally's glass
and
2x = amt to fill Bob's glass
then
total amt when mixed together = 3x
:
Sally's syrup = 1%2F3x
Bob's syrup = 1%2F4(2x) = 2%2F4x = 1%2F2x
:
1%2F3x + 1%2F2x =
2%2F6x + 3%2F6x = 5%2F6x; amt of syrup when mixed together
Find what part 3x is 5%2F6x?
:
The x's cancel so we have:
%285%2F6%29%2F3 = 5%2F6 * 1%2F3 = 5%2F18 of the total mixture is syrup