SOLUTION: A 2 bowl set has the following description: The lid is interchangeable. Weight of larger bowl: 12 oz. without lid. With lid, larger weighs twice as much as smaller withou

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Question 1201962: A 2 bowl set has the following description:
The lid is interchangeable.
Weight of larger bowl: 12 oz. without lid.
With lid, larger weighs twice as much as smaller without lid.
With lid, smaller weighs one third more than larger without lid.
Calculate weight of lid.
Let A = larger.
Let B = smaller.
Let C = lid.
A = 12.
A + C = 2(B).
A = 1/3(B + C)
Not sure if set up correctly and how to solve.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Choosing the variables differently, and following the description
small bowl           c
large bowl           12
lid                  x

The description then gives system%2812%2Bx=2c%2Cc%2Bx=12%2B%281%2F3%2912%29

system%2812%2Bx=2c%2Cc%2Bx=16%29

system%282c-x=12%2Cc%2Bx=16%29-----------VERY SIMPLE TO SOLVE (STEPS ARE STRAIGHTFORWARD!)

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These result values check as correct.
system%28x=6%262%2F3%2Cand%2Cc=9%261%2F3%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
A 2 bowl set has the following description:

The lid is interchangeable.

Weight of larger bowl:  12 oz. without lid.

With lid, larger weighs twice as much as smaller without lid.

With lid, smaller weighs one third more than larger without lid.

Calculate weight of lid.

Let A = larger.

Let B = smaller.

Let C = lid.

A = 12.

A + C = 2(B).

A = 1/3(B + C)

Not sure if set up correctly and how to solve.

Why did that other person bring in another variable, x? Doesn't the problem list enough variables?

A = 1/3(B + C) <==== This is WRONG!! Read on!

Weight of larger bowl, without lid: A = 12
Weight of larger bowl, with lid: A + C, or 12 + C

Weight of smaller bowl, without lid: B
Weight of smaller bowl, with lid: B + C

As larger, with lid, weighs twice as much as smaller without lid, we get: matrix%282%2C3%2C+12+%2B+C%2C+%22=%22%2C+2B%2C+2B+-+C%2C+%22=%22%2C+12%29 --- eq (i)

    As smaller, with lid, weighs 1%2F3 MORE than larger, without lid, we get: matrix%281%2C3%2C+B+%2B+C%2C+%22=%22%2C+1%261%2F3%28A%29%29
                                                                           matrix%281%2C3%2C+B+%2B+C%2C+%22=%22%2C+%284%2F3%29%2812%29%29 -- Substituting 12 for A                                          
                                                                           B + C = 16
                                                                               B = 16 - C ----- eq (ii)

                                                                   2(16 - C) - C = 12 ---- Substituting 16 - C for B in eq (i)
                                                                     32 - 2C - C = 12
                                                                        - 2C - C = 12 - 32                                                                        
                                                                            - 3C = - 20
                                                            Weight of lid, or