Step-by-step explanation:
first a little help, how they got the equations :
in total they need 15 liters.
so, whatever x and y are, but together they must be 15 L.
x + y = 15
then, we are mixing x liters of 20% alcohol with y liters of 100% alcohol, that have to result in a 40% solution of (x+y) liters :
0.2x + y = 0.4(x+y)
we know from the first equation that x+y = 15, so the second equation is actually
0.2x + y = 0.4 × 15 = 6
so, we have
x + y = 15
0.2x + y = 6
do you notice something ? there is a "+ y" in both equations.
so we can actually subtract the second equation from the first, eliminate y and solve for the remaining x. and then use one of the original equating to get also y :
x + y = 15
- 0.2x + y = 6
---------------------
0.8x 0 = 9
0.8x = 9
x = 9/0.8 = 11.25 liters
x + y = 15
11.25 + y = 15
y = 15 - 11.25 = 3.75 liters
