Question

Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0.04 liters. Then he wants to fill the tank with water until it's completely full. If he uses 50 marbles, he will have to add 33 liters of water.

What is the volume of the tank?

Andrei has exactly 20 liters of water. How many marbles does he need so the tank is full?

Answer 1

The necessary amount of water decreceas at the same rate over both intervals

Explanation:

I did it on khan academy

Answer 2

a). Volume of Tank=35 liters

b). Number of marbles=375 marbles

Explanation:

a).Volume of the Tank

For the tank to be full Andrei needs;

• 50 marbles each with a volume of 0.04 liters

Total volume of marbles=50×0.04=2 liters

• 33 liters of water

Total volume of water= 33 liters of water

The total volume of the tank=Total volume of marbles+Total volume of water=(33+2)=35 liters

b). How many marbles he needs when the tank is full.

Volume of Tank when full=Total volume of marbles+Total volume of water.....equation 1

Total volume of water is known=20 liters

Total volume when tank is full=35 liters and

Total volume of marbles=Number of marbles×volume per marble

Where Number of marbles is unknown=N, and volume per marbles=0.04 liters

Total volume of marbles=(N×0.04)

Substituting in equation below;

Volume of Tank when full=(Total volume of marbles)+(Total volume of water).....equation 1

35=(N×0.04)+(20)

(35-20)=(N×0.04)

Solving for N

(N×0.04)/0.04=15/0.04

N=375

N=Number of marbles=375 marbles