can't remember how to do these kinds of questions

Question

Jasmine and Paul are selling fruit for a school fundraiser. Customers can buy small and large boxes of oranges. Jasmine sold 3 small boxes and 9 large boxes for a total of $162. Paul sold 9 small boxes and 11 large boxes for a total of $246. Find the cost of each small box of oranges and each large box of oranges.

Answer 1

Hi Madison,

 

Let x = cost of small boxes

Let y = cost of large boxes

 

 

3x + 9y  = 162   (3 small, 9 large = $162

9x + 11y = 246  (9 small, 11 large = $246

 

now solve by eliminating one of the variables

 

multiply first equation by 3,   doing this so I will have 9x and I can then subtract and get rid of the x variable

 

9x + 27y = 486   (multiplied first equation by 3

9x + 11y = 246

 

now subtract  and you get

 

16y = 240

 

or y = 15 

 

now use this back in the original first equation and solve for x

 

3x + 9(15) = 162

 

3x + 135 = 162

 

3x = 27

 

x = 9

 

 

Hope this helps