Question

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?

I am in need of help

Answer 1

12 grams of 40% solution and 8 grams of 70% solution is your answer

Answer 2

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

Explanation:

Let x be the weight of 40% salt solution and y be the weight of 70% salt solution.

We have been given that Serena needs 20 grams of solution of salt. We can represent this information in an equation as:

`x+y=20...(1)`

We are also told that she needs 20 grams of a 52% solution of salt by adding 40% and 70% of salt solutions.

We can represent this information in an equation as:

`(40)/(100)*x+(70)/(100)*y=20*(52)/(100)...(2)`

`0.40x+0.70y=20*0.52...(2)`

Now we will use substitution method to solve our system of equations.

From equation (1) we will get,

`x=20-y`

Substituting this value in equation (2) we will get,

`0.40(20-y)+0.70y=20*0.52`

`8-0.40y+0.70y=10.4`

`8-8-0.40y+0.70y=10.4-8`

`0.30y=2.4`

`(0.30y)/(0.30)=(2.4)/(0.30)`

`y=8`

Therefore, Serena must use 8 grams of 70% salt solution.

Upon substituting y=8 in equation (1) we will get,

`x+8=20`

`x+8-8=20-8`

`x=12`

Therefore, Serena must use 12 grams of 40% salt solution.