SOLUTION: How many liters of a 35% acid solution should be mixed with a 14% solution to obtain 70 liters of a 20% acid solution?
A chemist wants to obtain 15 liters of 24% alcohol solutio
Algebra.Com
Question 95599: How many liters of a 35% acid solution should be mixed with a 14% solution to obtain 70 liters of a 20% acid solution?
A chemist wants to obtain 15 liters of 24% alcohol solution by combining a quantity of 20% solution, a quantity of 30% alcohol solution and 1 liter of pure water. How many liters of each of the alcohol solutions must be used?
How many kg each of scrap iron and steel containing 75% iron must be used to produce 15 kg of 8% steel rod?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
(1) How many liters of a 35% acid solution should be mixed with a 14% solution to obtain 70 liters of a 20% acid solution?
Let x=amount of 35% solution needed
Then70-x=amount of 14% solution needed
Now we know that the amount of pure acid in the 35% solution (0.35x) plus the amount of pure acid in the 14% solution (0.14(70-x)) has to equal the amount of pure acid in final mixture (0.20(70)). So our equation to solve is:
0.35x+0.14(70-x)=0.20(70) get rid of parens
0.35x+9.8-0.14x=14 subtract 9.8 from both sides
0.35x-0.14x+9.8-9.8=14-9.8 collect like terms
0.21x=4.2 divide both sides by o.21
x=20 liters--------------------amount of 35% solution needed
70-x=70-20=50 liters --------------amount of 14% solution needed
CK
0.35*20+0.14*50=0.20*70
7+7=14
14=14
(2) A chemist wants to obtain 15 liters of 24% alcohol solution by combining a quantity of 20% solution, a quantity of 30% alcohol solution and 1 liter of pure water. How many liters of each of the alcohol solutions must be used?
Amount of alcohol solutions plus the water =15 liters
Let x=the amount of 20% solution needed
Then 14-x=amount of 30% solution needed
Now we know that the amount of pure alcohol in the 20% solution (0.20x) plus the amount of pure alcohol in the 30% solution (0.30(14-x) plus the amount of pure alcohol in the water (0) equals (0.24*15). So our equation to solve is:
0.20x+0.30(14-x)=0.24*15 get rid of parens
0.20x+4.2-0.30x=3.6 subtract 4.2 from both sides
0.20x+4.2-4.2-0.30x=3.6-4.2 collect like terms
-0.10x=-0.6 divide both sides by -0.10
x=6 liters ------------------------amount of 20% solution needed
14-x=14-6=8 liters ---------------------amount of 30% solution needed
CK
0.20*6+0.30*8=0.24*15
1.2+2.4=3.6
3.6=3.6
(3) How many kg each of scrap iron and steel containing 75% iron must be used to produce 15 kg of 8% steel rod?
Let x=amount of steel containing 75% iron (and 25% steel) that's needed
Then 15-x=amount of pure iron (containing 0% steel) that's needed
Now we know that the amount of pure steel (0.25x)in the 75% alloy plus the amount of pure steel in the scrap iron (0) has to equal the amount of pure steel in the final steel rod (0.08(15)). So our equation to solve is:
0.25x=0.08*15 or
0.25x=1.2 divide both sides by 0.25
x=4.8 kg-------------------------amount of steel containing 75% iron that's needed
15-x=15-4.8=10.2 kg--------amount of scrap iron needed
Ck
0.25*4.8+0*10.2=0.08*15
1.2=1.2
Hope this helps----ptaylor
RELATED QUESTIONS
How many liters of 20% acid solution should be mixed with 50% acid solution to obtain 12... (answered by josgarithmetic)
how many liters of a 15% acid solution should be mixed with a 35% acid solution to make 7 (answered by josgarithmetic)
A chemist has 10% and 50% solutions of acid available. How many liters of each solution... (answered by solver91311)
How many liters of a 16% acid solution should be mixed with 20 liters of 50% acid... (answered by richwmiller)
How many liters of a 20% acid solution should be mixed with 30 liters of 50% acid... (answered by Boreal,stanbon)
How many liters of a 12% acid solution and a 20% acid solution should be mixed in order... (answered by mananth)
How many liters of a 10% solution of acid should be mixed with 60% solution of acid to... (answered by ewatrrr)
How many liters of a 15% acid solution should be mixed with 30 liters of a 40% acid... (answered by lostin)
Determine how many liters of a 10 percent acid solution and 25 percent acid solution... (answered by Alan3354)
How many liters of a 15% acid solution should be mixed with 10 liters of a 36% acid... (answered by josgarithmetic,greenestamps)