Graphing linear inequalities

Question

Sarxy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. Apples cost $.24 each and oranges cost $.80 each. She has $12 to spend and would like to purchase at least 20 pieces of fruit total. 

1) write a system of linear inequalities to represent this situation, then graph.

2) using your graph, give two possible combinations of apples and oranges Darcy can buy.

Answer 1

A + O = 20 --> O = 20 - A

 

24A +  80O = 1200 <--- amounts in pennies

 

 

24A + 80(20 - A) = 1200

 

24A + 1600 - 80A = 1200

 

-56A = -400

 

A = -400/-56 = 200/28 = 100/14 = 50/7

 

O = 20 - 50/7 = 140/7 - 50/7 = 90/7

 

CHECK:

  50/7 * 20 + 90/7 * 80 = 1000/7 + 7200/7 = 8200/7 = 1200 <--- which is $12 in pennies

 

50/7 = 7 and 1/7 apples

90/7 = 12 and 6/7 oranges

 

Now to address the inequality:

 

   # apples        # oranges         apples cost           oranges cost          total cost
         12                8                 $2.40                      $ 6.40                     $8.80
         13                9                 $2.60                      $7.20                      $9.80
         14              10                 $2.80                      $8.00                      $10.80
         15              11                 $3.00                      $8.80                      $11.80
         13              11                 $2.60                      $8.80                       $11.40