Answer: 160 liters of the
40% solution and 80 liters of the 70% solution will be used.
Step-by-step explanation:
Let x represent the number of liters of 40% antifreeze solution that should be used.
Let y represent the number of liters of 70% antifreeze solution that should be used.
The volume of the mixture to be mixed is 240 liters. It means that
x + y = 240
The 40% antifreeze solution is to be mixed with a 70% antifreeze
solution to get 240 liters of a 50% solution. This means that
0.4x + 0.7y = 0.5(240)
0.4x + 0.7y = 120 - - - - - - - - - - - -1
Substituting x = 240 - y into equation 1, it becomes
0.4(240 - y) + 0.7y = 120
96 - 0.4y + 0.7y = 120
- 0.4y + 0.7y = 120 - 96
0.3y = 24
y = 24/0.3
y = 80
x = 240 - y = 240 - 80
x = 160
Keep in mind that the positive directions of the two axis are: upwards for the y axis and rightwards for the x axis.
So, translating a point 6 units up means to go 6 units along the positive direction on the y axis. For this reason, the new y coordinate will be 6 units more than the old one.
Similarly, going 3 units left means to decrease by 3 the x coordinate, because we're following the negative direction.
So, to recap, this transformation maps 
This means that the two points become
I would say that 0.36 is 36/100.
