Weight

[Guest]

A double boiler has the following description:

The lid fits either pot.

The larger pot weighs 12 oz. without lid.

With lid it weighs twice as much as smaller pot without lid.

The smaller pot with lid weighs one third more than larger without lid.

Determine weight of lid alone.

Let L = larger pot.

S = smaller pot.

X = lid.

Not sure how to solve.

[Math Tutor]

"The lid fits either pot": This means that the weight of the lid is the same for both pots.
So, let's use X to represent the weight of the lid.

"The larger pot weighs 12 oz. without lid": Let's use L_wl to represent the weight of the larger pot without lid.
So, L_wl = 12.

"With lid it weighs twice as much as smaller pot without lid": Let's use S_wl to represent the weight of the smaller pot without lid.
So, L_wl + X = 2(S_wl).

"The smaller pot with lid weighs one third more than larger without lid": Let's use S_wl + X to represent the weight of the smaller pot with lid.
So, S_wl + X = 4/3 * L_wl.

Now we have four equations and four unknowns, so we can solve for X. Let's rearrange equation 3 to solve for S_wl:

S_wl = (L_wl + X) / 2

Substitute this expression for S_wl into equation 4:

(L_wl + X) / 2 + X = 4/3 * L_wl

Simplify and solve for X:

3(L_wl + X) + 6X = 8L_wl

3L_wl + 9X = 8L_wl

X = (8L_wl - 3L_wl) / 9

X = L_wl / 3

Substitute L_wl = 12:

X = 12 / 3

X = 4

Therefore, the weight of the lid alone is 4 oz.

[Guest]

A couple of questions:

1) Why was the one third changed to 4/3 ?

2) Explain the steps involving rearranging equation 3.

[Guest]

Please reply, Thanks.

[Guest]

Please respond. Thanks.

[Guest]

Someone please reply. Thanks.

[Guest]

Let's set up some equations based on the given information:

The larger pot (L) weighs 12 oz. without the lid:

L = 12 oz.

With the lid, the larger pot (L) weighs twice as much as the smaller pot (S) without the lid:

L + X = 2(S)

The smaller pot (S) with the lid weighs one third more than the larger pot (L) without the lid:

S + X = 4/3 L

We have three equations and three unknowns (L, S, and X), so we can solve for X (the weight of the lid) using algebra. First, we can simplify the second equation:

L + X = 2(S)
L + X = 2(L/2 + X)
L + X = L + 2X
X = L

Substitute X = L in the third equation:

S + X = 4/3 L
S + L = 4/3 L
S = 1/3 L

Now we can substitute both X = L and S = 1/3 L into the first equation:

L + X + S + X = total weight
12 + L + 1/3 L + L = total weight
4 L + 12 = total weight

We know that the total weight is the weight of the two pots plus the weight of the lid:

total weight = L + S + X + X = 12 + L + 1/3 L + L = 4 L + 12

So we can set the two expressions for the total weight equal to each other and solve for L:

4 L + 12 = total weight = 4 L + 2 X
2 X = 12
X = 6 oz.

Therefore, the weight of the lid alone is 6 oz.

[Guest]

Thanks.


" The smaller pot (S) with the lid weighs one third more than the larger pot (L) without the lid:

S + X = 4/3 L

We have three equations and three unknowns (L, S, and X), so we can solve for X (the weight of the lid) using algebra. First, we can simplify the second equation:

L + X = 2(S)
L + X = 2(L/2 + X)
L + X = L + 2X
X = L "

Questions:

1) Why is the 1/3 changed to 4/3 ?

2) Explain steps for simplifying 2nd equation.

Thanks.

[Guest]

Will someone answer my last 2 questions, please. Thanks.