EXPLANATION
Assuming that x represents the number of grams of 4% of salt solutions and y represents the number of grams of 14% of salt solution used, we can apply the following relationship:
(1) x + y = 990 //This is because the total required weight is 990 grams
As the weight of salt in the 12% final salt solution is equal to the sum of each amount of salt, we can use the following equation:
(2) x*4/100 + y*14/100 = 12/100 * 999
Simplifying:
0.04x + 0.14y = 119.88
Isolating y from (1):
y = 990 - x
Substituting in (2):
0.04x + 0.14(990-x) = 119.88
Applying the distributive property:
0.04x + 138.6 - 0.14x = 119.88
Adding like terms:
-0.1x + 138.6 = 119.88
Subtracting -138.6 to both sides:
-0.1x = 119.88-138.6
Subtracting like numbers:
-0.1x = -18.72
Dividing both sides by -0.1:
x = -18.72/-0.1
Simplifying:
x = 187.2
Substituting x in (1):
(1) 187.2 + y = 990
Subtracting 187.2 to both sides:
y = 990 - 187.2
Subtracting like numbers:
y = 802.8
In conclusion, the amount of grams of each solution is as follows:
4% salt solution --------> 187.2 grams
14% salt solution --------> 802.8 grams