Math question, please help!

Question

I do not get this, and no one in my family is here to help me, please help!

 

Jen and Chris are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Chris sold 3 small ones, ad 14 large ones for a total of $203. Jen sold 11 small ones and 11 large ones for $220. Find the cost of one small box and one large box.

Answer 1

Since when did they start teaching 2 x 2 systems of equations in 5th grade

my goodness.

 

Let S be the price of the small box and L be the price of the large box.

 

Chris:   3S + 14L = 203

Jen:     11S + 11L = 220

 

In the second equation, 11 can be factored out:

   11(S+L) = 220

   S + L = 220/11 = 20

 

 

So the system is now:

  3S + 14L = 203

  S + L = 20  ----> L = 20 - S

 

Substituting the second equation into the first.

 

  3S + 14 ( 20 - S) = 203

  3S + 280 - 14S = 203

 -11S + 280 = 203

 

  -11S = 203 - 280

 -11S = -77

 

S = -77/-11 = 7

So the small box costs $7.

The large box costs $20 - $7 = $13

 

CHECK:

  3 x 7 + 14 x 13 = 21 + 182 = 203

  11 x 7 + 11 x 13 = 77 + 143 = 220