A company uses a new machine and an old machine to print booklets. Each machine

Question

A company uses a new machine and an old machine to print booklets. Each machine prints booklets at a constant rate. The graph and the equation represent the relationships between x, the number of minutes the machines print, and y, the number of booklets printed. The company uses both machines to print a total of 1, 250 booklets. Both machines start printing at the same time. During printing, the old machine breaks down and stops printing. The new machine continues printing for an additional 14 minutes and completes the order. What is the total number of minutes the new machine prints? Show or explain all your work. Enter your answer and your work in the space provided.

Explanation / Answer

Step 1:

Find the Equation for New Machine.

It is of the form y = kx as the graph is linear and passes through the origin.

Substituting the value of (x,y) from the graph, we can get the value of k.

Substituting the point (6,75) , we get k = 75/6 = 12.5

Therefore, the equation for new machine is

Step 2 :

After the old machine stops, the new machine runs for 14 more minutes.

The total booklets printed in the 14 minutes is given by

175 books were printed in 14 minutes by the new machine

So 1250 - 175 = 1075 books were printed earlier

Step 3:

Calculate the run time of the machines earlier.

The total booklets printed when the machines ran together will be the sum of the prints of both the machines.

Therefore ,

Therefore, the machines ran together for 50 minutes and the new machine ran for 14 more minutes.

Thus, the new machine ran for 50 +14 = 64 minutes totally.

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