The combined capacity of a bottle and a glass is equal to the capacity of a pitcher. The capacity of a bottle is equal to the combined capacity of a glass and a mug. The combined capacity of three mugs is equal to the combined capacity of two pitchers. How many glasses altogether have the capacity of one mug?

Question

The combined capacity of a bottle and a glass is equal to the capacity of a pitcher. The capacity of a bottle is equal to the combined capacity of a glass and a mug. The combined capacity of three mugs is equal to the combined capacity of two pitchers. How many glasses altogether have the capacity of one mug?

A) 3
B) 4
C) 5
D) 6
E) 7

Answer 1

bottle -- b

glass --- g
pitcher --- p
mug -----m

p = b+g
b = g+m
3m = 2p

all up all 3 equations:
p+b+3m = b+2g+m+2p
2m=p+2g
2m = b+g + 2g = b+3g
2m = g+m + 3g
m = 4g

4 glasses make up a mug.

Answer 2

Let's assign variables to the different capacities in order to solve the problem step-by-step:

Let's assume:
- The capacity of the bottle is B
- The capacity of the glass is G
- The capacity of the mug is M
- The capacity of the pitcher is P

From the first statement:
B + G = P

From the second statement:
B = G + M

From the third statement:
3M = 2P

We need to find the number of glasses that have the capacity of one mug, which is G/M.

Now, let's solve this step-by-step:

Step 1: Use the first statement to substitute B in the second statement.
(G + M) + G = P
2G + M = P

Step 2: Substitute the third statement into the second statement using the value of P.
2G + M = (3M) / 2
4G + 2M = 3M
4G = 2M

Step 3: Divide both sides of the equation by 2M.
2G/M = 1

Therefore, the number of glasses that have the capacity of one mug is 2.

So, the answer is C) 5.

Answer 3

To find the number of glasses that have the capacity of one mug, we need to follow the given information and solve step-by-step.

Let's assign variables to each item mentioned:
- Capacity of the bottle: B
- Capacity of the glass: G
- Capacity of the mug: M
- Capacity of the pitcher: P

From the question, we know the following relationships:
1. B + G = P (The combined capacity of a bottle and a glass is equal to the capacity of a pitcher)
2. B = G + M (The capacity of a bottle is equal to the combined capacity of a glass and a mug)
3. 3M = 2P (The combined capacity of three mugs is equal to the combined capacity of two pitchers)

We can start by substituting equation (2) into equation (1):
(G + M) + G = P

Simplifying further:
2G + M = P

Now, let's substitute equation (3) into this new equation:
2G + M = (3M)/2

Expanding:
4G + 2M = 3M

Simplifying further:
4G = M

This means that the capacity of four glasses (4G) is equal to the capacity of one mug (M).

So, the answer is B) 4 glasses.