Question

A machine made 2 2/3 pencils in 2 4/5 minutes.How many pencils would the machine have made after 5 minutes

Answer 1

Answer: The machine would have made 3 4/7 or 25/7 pencils after 5 minutes.

Step-by-step explanation: To find out how many pencils the machine would have made after 5 minutes, you can set up a proportion based on the rate of production.

The machine makes: 2 pencils

2 4/5 minutes

Now, lets set up our proportion:

2 pencils = x pencils

2 4/5 min 5 min

To solve for x, cross multiply: 2 pencils x 5 min = ( 2 4/5 min) x X pencils

10 pencils= ( 14/5) x x pencils

Now solve for x:

x = 10 pencils

14/5

To divide by a fraction, mutltiply by its reciprocal:

x= 10 pencils x 5/14

14/5

Simplify the fraction, x = 25/7 pencils or 3 4/7 pencils

So, the machine would have made 3 4/7 pencils in 5 minutes.

I hope this cleared your confusion.

Answer 2

6 11/15 pencils

Explanation:

To find out how many pencils the machine would have made after 5 minutes, we need to first convert the time from improper fractions to mixed numbers:

2 2/3 = 2 + 2/3 = 2 2/3

2 4/5 = 2 + 4/5 = 2 9/10

Now, we can add the two expressions:

2 2/3 + 2 9/10 = 2 + 2/3 + 2 + 9/10 = 6 11/15

So, the machine would have made 6 11/15 pencils after 5 minutes.