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?

Question

contestada

Respuesta :

ranikashyab066 ranikashyab066 · Answer 1 · 2020-04-16T09:49:37+02:00

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)