Serena is making an experiment. for that, she needs 20 grams of a 52% solution of salt. she has two large bottles of salt water: one with 40% and the other with 70% of salt in them. how much of each must she use to make the solution she needs?

This is a simple algebraic problem, specifically for the mixture type of problem. Let x be the mass of 40% solution and y be the mass of 70% solution. The first equation would then be:

x + y = 20 --> eqn 1

The second equation would be the mass balance shown below:

(x)(0.40) + y(0.70) = 20(0.52) --> eqn 2

Rearranging eqn 1,
x = 20 - y
Substitute this to eqn 2:

(20 - y)(0.40) + y(0.70) = 20(0.52)
Solve for y,
y = 8 grams
 
Finally, solve for x.
x = 20 - 8 = 12 grams

Therefore, Serena needs 12 grams of the 40% solution and 8 grams of the 70% solution.