Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of orange and large boxes of orange. Matt sold 11 small boxes of orange and 11 large boxes of orange for a total of $220. Find the cost each of one small boxes of orange and one large boxes of orange

Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small(?) boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.

Answer:

Cost of one small box is $7 and cost of one large box is $13

Explanation:

Given:

Cost of 11 small boxes and 11 large small boxes of oranges sold by Ming=$220

Cost of 3 small boxes and 14 large small boxes of oranges sold by Matt=$203

To Find:

Cost of one small orange box=?

Cost of one large orange box=?

Solution:

Let the cost of one small box be $a

Cost of one big box be $b.

Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203

Then,

3 x $a + 14 x $b = $203

3a + 14b = 20………………………………..(1)

Ming sold 11 small boxes of orange and 11 large boxes of orange for a total of $220.

Then,

11 x $a + 11 x $b = $220

11a + 11b = 220

a + b = 20……………………………………(2)

Now, solving the above equations,

From equation(2) we get

a = 20 – b

So, put value of a in (1)

3(20 – b) + 14b = 203

60 – 3b + 14b = 203

11b = 203 – 60

11b = 143

[tex]b = \frac{143}{11}[/tex]

b=13

Thus,

a = 20 – 13 = 7

a=7