King’s Service Station uses two kinds of cleaning solution containing acid and water. “Attack” is 2% acid and “Blast” is 6% acid. They want to mix the two to get 60qt of a solution that is 5% acid. How many quarts of each should they use.
Let a = number of quarts of "Attack"
Let b = number of quarts of "Blast"
.02a+.06b=amount of acid=.05(a+b)
and, a+b=60
To find how many quarts of each solution King's Service Station should use, we can set up a system of equations based on the given information.
1. The total amount of the solution is 60 quarts:
a + b = 60
2. The percentage of acid in the final solution is 5%:
(2% acid in Attack) * a + (6% acid in Blast) * b = (5% acid in final solution) * 60
Now, let's solve this system of equations.
First, rearrange equation 1 to isolate a:
a = 60 - b
Substitute this value of a into equation 2:
(2/100)(60 - b) + (6/100)(b) = (5/100)(60)
Simplify the equation:
(120 - 2b + 6b)/100 = 3
Combine like terms:
4b + 120 = 300
Subtract 120 from both sides:
4b = 180
Divide both sides by 4:
b = 45
Now substitute the value of b back into equation 1 to find a:
a + 45 = 60
a = 60 - 45
a = 15
Therefore, King's Service Station should use 15 quarts of "Attack" and 45 quarts of "Blast" to obtain a 60-quart solution with 5% acid.