How many grams each of a 10% salt solution and a 5% salt solution
must be mixed in order to obtain 400 g of an 8% solution?
Answers
Answer:
You need to add 100 g of the 20% salt solution.
Step-by-step explanation:
So, you're dealing with two salt solutions of different percent concentrations by mass.
Start by calculating how much salt you get in the 400-g sample of the 10% solution.
m
salt
m
solution
⋅
100
=
10
%
m
salt
=
10
⋅
m
solution
100
m
salt
=
10
⋅
400
100
=
40 g salt
Now, let's say that the mass of the 20% solution needed is equal to
x
grams. SInce this solution has 20 g of salt for every 100 g of solution, you can say that
x
g solution
⋅
20 g salt
100
g solution
=
20
100
x
=
x
5
g salt
The taol mass of the salt in the target 12% solution will be
m
salt
=
40
+
x
5
The total mass of the target solution will be
m
sol
=
400
+
x
This means that you can write
(
40
+
x
5
)
g salt
(
400
+
x
)
g solution
⋅
100
=
12
%
Rearrange and solve this equation for
x
to get
(
40
+
x
5
)
⋅
100
=
12
⋅
(
400
+
x
)
4000
+
20
x
=
4800
+
12
x
8
x
=
800
⇒
x
=
800
8
=
100 g
This means that if you add 100 g of the 20% solution to 400g of the 10% solution, you will get 500 g of a 12% salt solution.