If we have x liters of the 40% salt solution (composed of pure salt plus other stuff) then we have exactly 0.40*x liters of pure salt. Simply multiply the decimal form of the percentage with the amount of solution.
Similarly, if we have y liters of the 20% solution, then we have 0.20*y liters of pure salt
Combined, we have 0.40*x + 0.20*y liters of pure salt all together.
We want 1500 liters of a 28% solution, so we want 1500*0.28 = 420 liters of pure salt
Equate the two expressions (0.40*x + 0.20*y and 420) to get 0.40*x + 0.20*y = 420
We have the equation 0.40*x + 0.20*y = 420 and we also know that y = 1500-x
Let's use the substitution property now
0.40*x + 0.20*y = 420 0.40*x + 0.20*( y ) = 420 0.40*x + 0.20*( 1500 - x ) = 420 ... note how y is replaced with 1500-x
Now we can solve for x 0.40*x + 0.20*( 1500 - x ) = 420 0.40*x + 0.20*(1500) + 0.20*(-x) = 420 0.40*x + 300 - 0.20x = 420 0.40*x - 0.20x + 300 = 420 0.20x + 300 = 420 0.20x + 300 - 300 = 420 - 300 0.20x = 120 0.20x/0.20 = 120/0.20 x = 600
Now that we know x, use this to find y y = 1500-x y = 1500-600 ... plug in x = 600 (ie replace x with 600) y = 900 --------------------------------------------------- ---------------------------------------------------
Answers:
We need 600 liters of the 40% solution We need 900 liters of the 20% solution
The probability of both dice having the same number is 636, as there are 36 different outcomes, 6 of which have two of the same number, i.e. (1,1),(2,2),....
The expected number of rolls of this type in 100 pairs of dice rolls is 100∗636
