pre calc homework question on liters

Question

Tank A initially contains 60 liters of water with 1800 grams of salt dissolved in it. Tank B contains a saltwater solution with a concentration of 50 grams per liter. A valve is opened, and the solution in tank B begins to pour into tank A.

What is the concentration of salt in tank A (in grams per liter) after 30 liters of the tank B solution have been poured into it? (Round your answer to the nearest tenth of a gram per liter.)

Answer:  grams per liter

How much of the tank B solution must be poured into tank A for the salt concentration in tank A to reach 40 grams per liter? (Round your answer to the nearest tenth of a liter.)

Answer:  liters

Answer 1

Let's calculate how much salt is moved from tank B to tank A: if salt concentration in B is 50 grams per liter, and 30 liters of this tank is transferred to tank A, then the amount of salt transferred is 50 (gr/lit) * 30 (lit) = 1500 grams of salt which is now in tank A. So tank A now has a total of 1800+1500=3300 grams of salt. Its total volume is also increased by the 30 liters which has come from tank B, so tank A now has 60+30=90 liters of water.

Therefore, tank A now has 3300 grams of salt in 90 liters of water, so the new concentration is 3300/90=110/3=36.7 gram/liter.

For the second part you can set up an equation to represent amount of salt in tanks A and B before mixing and the right side would be the amount in tank A after mixing; x represents amount of liters to be moved from tank B to A:

[to get amount of salt you multiply concentration by the volume, hence 50x for tank B below and 40(x+60) from tank A after mixing]

1800 (gr salt in tank A) + 50x (gr salt in tank B) = 40(x+60) salt in A after mixing

Note that the volume of A after mixing would be x+60 (the original 60 in A plus the x liters coming from B)

Well, this is an easy equation to solve by combining like terms and isolating x: 1800+50x=40x+2400

10x=600; x=60 liters. So you need to move 60 liters of the solution from B to A to achieve the desired result.

Hope it's all clear!