Question 1044237
pl = price of lemonade.
po = price of orange juice.


she believes she can sell:


50 + 10 * pl - 20 * po glasses of orange juice per day.
100 - 30 * pl + 10 * pl glasses of lemonade per day.


since number of glasses of orange juice per day = 20 and number of glasses of lemonade per day = 90, you get 2 equations that need to be solved simultaneously.


they are:


50 + 10 * pl - 20 * po = 20
100 - 30 * pl + 10 * pl = 90


move all the constants over to the right side of the equation.


first equation becomes 10 * pl - 20 * po = 20 - 50
second equation becomes -30 * pl + 10 * po = 90 - 100


simplify to get:


10 * pl - 20 * po = -30
-30 * pl + 10 * po = -10


multiply both sides of the second equation by 2 and leave the first equation as is to get:


10 * pl - 20 * po = -30
-60 * pl + 20 * po = -20


add both equations together to get:


-50 * pl = -50


solve for pl to get pl = 1


replace pl by 1 in either equation and solve for po to get po = 2.


your solution is that pl = 1 and po = 2.


you can confirm by replacing pl with 1 and po with 2 in your original equations to see if the equations hold true.