Question

Three vases have different sizes. the capacity of the big vase is half times bigger than the capacity of the middle sized vase. the capacity of the middle sized vase is four times bigger than the capacity of the small vase

mark the capacity of the middle vase as x


1. what is the capacity of the big vase (in x?)


2.what is the capacity of the small vase (in x?)


3.all of the 3 vases together have a capacity of 5,5 liters. What is the capacity of the middle vase in liters


middle = x


big = 1/2x + x


small = x/4 I need some help T^T

Answer 1

The capacity of the big vase is half times bigger than the capacity of the middle sized vase, which means it is 1 + 1/2 times the capacity of the middle vase.

So, the capacity of the big vase in terms of x is:

1/2x + x = 3/2x

Therefore, the capacity of the big vase in x is 3/2x.

The capacity of the middle sized vase is four times bigger than the capacity of the small vase, which means it is 4 times the capacity of the small vase.

So, the capacity of the small vase in terms of x is:

x/4

Therefore, the capacity of the small vase in x is x/4.

The total capacity of the three vases is 5.5 liters. We can set up an equation based on this information:

x + 3/2x + x/4 = 5.5

Multiplying both sides by 4 to eliminate the fraction:

4x + 6x + x = 22

11x = 22

x = 2

Therefore, the capacity of the middle sized vase is 2 in terms of x. To find the capacity in liters, we can substitute x = 2 into any of the expressions we found earlier:

Capacity of the big vase: 3/2x = 3/2 * 2 = 3 liters

Capacity of the small vase: x/4 = 2/4 = 0.5 liters

So, the capacities of the three vases are 3 liters, 2 liters, and 0.5 liters, and their total capacity is 5.5 liters.