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Evie has a piece of ribbon that is 80 cm long. She cuts it into lengths with no ribbon left over. Each length is exactly 8.5 cm or 12.5 cm. How many of each length does Evie have?

Answer :

Using a function to express the number of pieces of the two lengths, Evie should have 3 pieces of ribbon of length 12.5 cm and 5 pieces of ribbon of length 8.5 cm.

In mathematics, a function is the representation of the relationship of a set of input(X) and its corresponding output(Y).

If Evie has a price of ribbon that is 80cm long that she wants to cut into lengths of exactly 8.5cm or 12.5cm and that no ribbon left over, then the function for this statement is:

12.5x + 8.5y = 80 ⇒ y = (80 - 12.5x)/8.5

where x is the number of pieces of length 12.5 cm and y is the number of pieces of length 8.5 cm, and x and y must be whole numbers(pieces of ribbon)

Listing down the possible integers for the value of x and solving for the corresponding y value.

x = 1 , y = 135/17

x = 2 , y = 110/17

x = 3 , y = 5

x = 4 , y = 60/17

x = 5 , y = 35/17

x = 6 , y = 10/17

Since when x = 3, y = 5 is the only ordered pair that is both integers, then it is the answer.

Learn more about functions here: https://brainly.com/question/25638609

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Rewritten by : Barada