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?

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)

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8