SOLUTION: (1) Tina is trying to determine the prices in dollars she should charge for lemonade (PL) and orange juice (PO) at her lemonade stand. She believes she can sell 50 + 10(PL)

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Question 1044237: (1) Tina is trying to determine the prices in dollars she should charge for lemonade (PL) and orange juice (PO) at her lemonade stand. She believes she can sell 50 + 10(PL) - 20(PO) glasses of orange juice per day and 100 - 30(PL) + 10(PO) glasses of lemonade per day. If Tina wants to sell 20 glasses of orange juice per day and 90 glasses of lemonade per day, what prices should she charge?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

SOLUTION: (1) Tina is trying to determine the prices in dollars she should charge for lemonade (PL) and orange juice (PO) at her lemonade stand. She believes she can sell 50 + 10(PL) - 20(PO