Question

The total combined volume of a glass, a jar, and a pitcher is 54 liters. If the jar has the same volume as 3 glasses and the pitcher has the same volume as 5 glasses, what is the volume of the glass?

Answer 1

Answer:

6 liters.

Step-by-step explanation:

So we have a glass, a jar, and a pitcher and together, they hold 54 liters.

We are told that the jar has the same volume as 3 glasses and the pitcher has the same volume as 5 glasses. In other words, let g denote glasses, j denote jars, and p denote pitchers:

$g+j+p=54$

Since  jar is the same as 3 glasses, this means that j=3g. And since the pitcher is the same as 5 glasses, this means that p=5g. Substitute:

$g+(3g)+(5g)=54$

Combine like terms:

$9g=54$

Divide both sides by 9. The left cancels:

$(9g)/9=54/9\\g=6$

Therefore, the volume of the glass is 6 liters.

Answer 2

Answer:

$\Large \boxed{\sf 6 \ liters}$

Step-by-step explanation:

Let the volume of the glass be x.

Let the volume of the jar be y.

Let the volume of the pitcher be z.

$\sf y = 3x \\\\z = 5x$

$\sf x + y + z = 54$

Substitution method.

$\sf x+3x+5x=54$

Combining like terms.

$\sf 9x = 54$

Dividing both sides by 9.

$\sf x = 6$

The volume of the glass is 6 liters.