Find the cost of each of one small box of tangerines and one large box of tangerines

Question

Chelsea and Danielle are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Danielle sold 3 small boxes of tangerines and 4 large boxes of tangerines for $103. Chelsea sold 6 small boxes of tangerines and 7 large boxes of tangerines for a total of $187. Fund the cost of each one of small tangerines and one large box of tangerines.

Answer 1

Set the cost of a small box of tangerines = x and the cost of a large box of tangerines = y

 

Danielle sold 3 small boxes and 4 large boxes for a total cost of $103. Therefore,

3x + 4y = 103

(the cost of 3 small boxes plus the cost of 4 large boxes equals $103)

 

 

Chelsea sold 6 small boxes and 7 large boxes totaling $187. Therefore,

6x + 7y = 187

(the cost of 6 small boxes plus the cost of 7 large boxes equals $187)

 

 

Now you have two equations and 2 unknowns, so you can solve for x and y

3x + 4y = 103

6x + 7y = 187

 

Using the elimination method, multiply the top equation by 2

2 (3x + 4y = 103)  →  6x + 8y = 206

 

Then subtract the two equations

  6x + 8y = 206

- 6x + 7y = 187

  0x +  y  = 19

 

Now that you know y = 19, you can substitute that into one of the two original equations.

Substituting y = 19 into the first equation give you

3x + 4(19) = 103

3x + 76 = 103

3x = 27

x = 9

 

Final Answer:

The small boxes of tangerines, x, cost $9.

The large boxes of tangerines, y, cost $19.