The total capacity of 6 pitchers and 12 glasses is 21 liters. The capacity of a pitchers if 5 times that of a glass. Find the capacity of each glass in liters.
let x = glass capacity
6(5x) + 12x = 21
Solve for x.
Let's solve this problem step by step.
First, let's assume the capacity of a glass is "x" liters.
According to the given information, the capacity of a pitcher is five times that of a glass. Therefore, the capacity of a pitcher is 5x liters.
Now, let's calculate the total capacity of all the pitchers and glasses.
Since there are 6 pitchers, the total capacity of the pitchers is 6 times the capacity of a pitcher, which is 6 * 5x = 30x liters.
Similarly, since there are 12 glasses, the total capacity of the glasses is 12 times the capacity of a glass, which is 12 * x = 12x liters.
According to the problem statement, the total capacity of all the pitchers and glasses is 21 liters. Therefore, we can write the equation:
Total capacity of pitchers + Total capacity of glasses = 21 liters
Substituting the values we found earlier, the equation becomes:
30x + 12x = 21
Simplifying the equation:
42x = 21
Now, divide both sides of the equation by 42 to solve for x:
x = 21 / 42
x = 0.5
Therefore, the capacity of each glass is 0.5 liters.