Ethan and Emily went shopping at a local farmers' market. They both bought the same type of apples and potatoes at the same stand. Ethan paid $25.50 for 8 pounds of apples and 5 pounds of potatoes. Emily paid $18.50 to buy 3 pounds of apples and 10 pounds of potatoes. Which ordered pair represents the price per pound of apples, x, and potatoes, y?

Ordered pair representing the price per pound of apples, x, and potatoes, y is (2.5, 1.1).

Step-by-step explanation:

Let us assume that the cost of per pound of apples = $ x

Assume that the cost of per pound of potatoes = $ y

Now, according to question:

The cost of 8 pounds of apples and 5 pounds of potatoes = $25.50

⇒ Cost of 8 pounds of Apple + Cost of 5 pounds of potatoes = $25.50

⇒ 8 x (Cost of 1 pound apple) + 5 x (cost of 1 pound potato) = $25.50

⇒ 8 x + 5 y = $25.50 ... (1)

⇒ 5 y = 25.5 - 8 x

Similarly,

The cost of 3 pounds of apples and 10 pounds of potatoes = $18.50

⇒ 3 x + 10 y = $18.50 ... (2)

or, 1.5 x + 5 y = $ 9.25 (dividing the equation by 2)

⇒ 5 y = 9.25 - 1.5 x

Now, comparing both equations, we get:

25.5 - 8 x = 9.25 - 1.5 x

⇒ 25.5 - 9.25 = 8 x - 1.5 x

⇒ 16.25 = 6.5 x

⇒ x = 2.5

Putting this value of x in 5 y = 9.25 - 1.5 x, we get:

5 y = 9.25 - 1.5 (2.5)

⇒ 5 y = 5.5

⇒ y = 1.1

So, the cost of 1 pound of apples = $2.5

The cost pf 1 pound of potatoes = $1.1

The ordered pair (x, y) is given as : (x, y) = (2.5,1.1)