Answer:
10 litres of the 27% acid solution is needed
Step-by-step explanation:
In this question, we are tasked with calculating the amount in litres of the 27% solution that Mr. Costa will need
we proceed as follows;
let us suppose Acosta needs X lts of 27%solution and Y lts of 32% solution to make 50L of 31% acid solution.
So total sum of x and y is 48
x + y = 50 ...............................(i)
amount of acid in 27% solution is 0.27Y
amount of acid in 32% solution is 0.32Y
Total amount of acid in 50 liters of 31% solution is 50 × 0.31 = 15.5
So 0.27x + 0.32y = 15.5 ..................................(ii)
From i, we can say y = 50 -x , we then substitute this into 2 to yield the following;
0.27x + 0.32(50 - x) = 15.5
0.27x + 16 - 0.32x = 15.5
⇒ 0.32x - 0.27x = 16 - 15.5
0.05x = 0.5
x = 0.5/0.05
x =10
Hence, 10 litres of the 27% acid solution is needed
