Define two variables. Write a system of equations, and then solve. In a chemistry lab, you have two vinegars. One is 5% acetic acid and one
is 6.5% acetic acid. You want to make 60 L of a vinegar with 6% acetic
acid. How many liters of each do you need?

Step-by-step explanation:

Assume that the amount needed from the 5% acid is x and that the amount needed from the 6.5% acid is y.

We are given that:

The volume of the final solution is 200 ml

This means that:

x + y = 200

This can be rewritten as:

x = 200 - y > equation I

We are also given that:

The concentration of the final solution is 6%

This means that:

5%x + 6.5%y = 6% (x+y)

This can be rewritten as:

0.05 x + 0.065 y = 0.06 (x+y) > equation II

Substitute with equation I in equation II and solve for y as follows:

0.05 x + 0.065 y = 0.06 (x+y)

0.05 (200-y) + 0.065 y = 0.06 (200-y+y)

10 - 0.05 y + 0.065 y = 12

0.015y = 12-10 = 2

y = 2/0.015

y = 133.3334 ml

Substitute with the y in equation I to get the x as follows:

x = 200 - y

x = 200 - 133.3334

x = 66.6667 ml

Based on the above calculations:

The amount required from the 5% acid = x = 66.6667 ml

The amount required from the 6.5% acid = y = 133.3334 ml

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this