Brain Teasers
Pots
You have two pots which fit the same lid. The large pot is 12 ounces without the lid. With the lid it weighs twice as much as the small pot on its own. The small pot with the lid is one-third more than the large pot on its own.
(1) How much does the lid weigh?
(2) How much does the small pot weigh?
(1) How much does the lid weigh?
(2) How much does the small pot weigh?
Answer
The lid weighs 6 2/3 ounces and the small pot weighs 9 1/3 ounces.Let us call the large pot P, the small pot p, and the lid L. The equations we are given then translate to:
1) P=12
2) P+L=2p
3) p+L=P+P/3
Combining the first two equations, we get:
4) 12+L=2p
Combining the second two, we get:
5)p+L=12+12/3
p+L=16
Simplifying equation two, we get:
6) p=P/2 +L/2
Adding L to each side gets:
P/2+L/2+L=p+L
Combining this with equation five gets:
7) P/2+L/2+L=P+P 1/3
P/2+L/2+L=16
Going back and adding in equation 1 gets:
8) 12/2+L/2+L=16
6+ L/2+L=16
Subtracting 6 from each side gets:
9) L/2+L=10
1.5L=10
To simplify this:
10) L=10/1.5
L=6 2/3
To figure out p is a simpler matter. Combining equations 4 and 10 gets:
11) 12+6 2/3=2p
18 2/3=2p
Simplifying this gets:
12) p=18 2/3 / 2
p=9 1/3
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Comments
Pretty fun to do, but it was kind of easy.
I liked it because it reminded me how to solve those pesky x and y problems!
Your method of solving is too cumbersome. We start at the same but solve the equations differently.
1. P=12
2. P+L=2p
3. p+L=P*4/3
Substitue 12 for P in each equation
4. 12+L=2p -> 12=2p-L
5. p+L=16 -> 16=p+L
Add the equations together
6. 28=3p -> p=9 1/3
Substitue for p in equ. 2
7. 12+L=2(9 1/3) -> L=6 2/3
1. P=12
2. P+L=2p
3. p+L=P*4/3
Substitue 12 for P in each equation
4. 12+L=2p -> 12=2p-L
5. p+L=16 -> 16=p+L
Add the equations together
6. 28=3p -> p=9 1/3
Substitue for p in equ. 2
7. 12+L=2(9 1/3) -> L=6 2/3
I agree with Fasil. MUCH to cumbersome. In fact I just started with 2 variables using 12 as its own number from the start. 2 variables; 2 equations; substitution; Bingo. fun but easy. Thanks
i have only ever seen more 'p's in a roast dinner
simple algebra...made me feel smart though
it was alright
Since I did it in my head, I KNOW the given solution makes the problem harder than it is.
The little pot with the lid is 16 ounces, so if x is the lid:
12 + x = 2(16 - x)
12 + x = 32 - 2x
3x = 20
x = 20/3 = 6 2/3
and the little pot is 16 - 6 2/3 = 9 1/3.
The little pot with the lid is 16 ounces, so if x is the lid:
12 + x = 2(16 - x)
12 + x = 32 - 2x
3x = 20
x = 20/3 = 6 2/3
and the little pot is 16 - 6 2/3 = 9 1/3.
This is a good problem for juniors who are not familiar with simultaneous equations. They will have to think carefully about how to form the equation using only 1 variable.
Good teaser but the given solution is way too complicated.
Good teaser but the given solution is way too complicated.
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