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Kaspar is buying apples and oranges from the market. The total cost of 4 apples and 3 oranges is $11, while the total cost of 2 apples and 5 oranges is $13. What is the cost of each apple and each orange?

 Nov 16, 2023
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Kaspar is buying apples and oranges from the market. The total cost of 4 apples and 3 oranges is $11, while the total cost of 2 apples and 5 oranges is $13. What is the cost of each apple and each orange?  

 

                                                  4A + 3G  =  11     (eq 1)  

                                                  2A + 5G  =  13     (eq 2) 

 

Multiply (eq 2) by 2                    4A + 10G  =  26   (eq 3)  

 

Subtract (eq 1) from (eq 3)                  7G  =  15  

                                                              G  =  15 / 7  =  2.14   (one orange)  

 

Plug the value of an orange  

back into (eq 1)                          4A + (3)(2.14)  =  11  

                                                                     4A  =  11 – 6.42  =  4.58  

                                                                       A  = 4.58 / 4  =  1.14   (one apple)  

 

Check answers  

(eq 1)                            4 • (1.14) + 3 • (2.14)  =  10.98   close enough to 11  

(eq 2)                            2 • (1.14) + 5 • (2.14)  =  12.98   close enough to 13  

 

The answers check out, considering that the calculations required rounding.  

.

 Nov 17, 2023

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