Answer:
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
Explanation:
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Let x be the number of liters of the 45% acid solution
The number of liters of the 70% acid solution is y
x + y = 50
x = 50 - y
Also
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?
We have:
45% × x + 70% × y = 65% × 50
0.45x + 0.70y = 0.65 × 50
0.45x + 0.70y = 32.5
We substitute x = 50 - y in the equation
0.45(50 - y) + 0.70y = 32.5
= 22.5 - 0.45y + 0.70y = 32.5
= - 0.45y + 0.70y = 32.5 - 22.5
= 0.25y = 10
Divide both sides by 0.25
= y = 10/0.25
y = 40 liters
x = 50 - y
x = 50 - 40
x = 10 liters
Hence,
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters