If I buy 2 apples and 6 oranges, I will spend $5.60. However, if I buy 6 apples and 2 oranges, I will spend $4.80. How much does one orange cost? Write the answer like this example: 48cents.

apples- 55 cents

oranges- 75 cents

To find the cost of one orange, we need to set up a system of equations based on the given information. Let's assume that the cost of one apple is represented by 'a' and the cost of one orange is represented by 'o'.

According to the problem, if 2 apples and 6 oranges are bought, the total cost is $5.60. This can be written as:

2a + 6o = 5.60 (Equation 1)

Similarly, if 6 apples and 2 oranges are bought, the total cost is $4.80. This can be written as:

6a + 2o = 4.80 (Equation 2)

Now, we have a system of equations (Equation 1 and Equation 2) that we can solve to find the value of 'o' (the cost of one orange).

To solve this system of equations, we can use substitution or elimination method. In this case, let's use the elimination method.

Multiplying Equation 1 by 3 and Equation 2 by 1, we get:

6a + 18o = 16.80 (Equation 3)
6a + 2o = 4.80 (Equation 2)

Now, subtracting Equation 2 from Equation 3, we have:

(6a + 18o) - (6a + 2o) = 16.80 - 4.80
16o = 12.00

Dividing both sides by 16, we get:

o = 12.00 / 16
o = 0.75

So, the cost of one orange is $0.75 or 75 cents.