a company machine makes 24 copies per minute. How many copies does it make in 4 minutes and 45 seconds?

Question

mathstudent55 · Answer

How many seconds are there in a minute?

anonymous · Answer

Break up the problem into steps. Use your fingers to count these out and it might help. In the first minute, the machine made 24 copies. In the next minute, the machine made another 24 copies,...and so on. Keep track of it on paper. Now the hard part is calculating how many copies were made in 45 seconds. You'll need to multiple 24 by a fraction. The fraction is 45/60. There are 60 seconds in a minute. So 24 x (45/60) would be the number of copies made in the 45 seconds.

mathstudent55 · Answer

There are 60 seconds in a minute.
Since the machine makes 24 copies per minute, that means it makes 24 copies in 60 seconds.

Now let's convert 4 minutes and 45 seconds into seconds.
Since there are 60 seconds in 1 minute, there are 4 * 60 seconds in 4 minutes.
4 minutes = 240 seconds
4 minutes and 45 seconds = 240 seconds + 45 seconds = 285 seconds

Now we use a proportion.
24 copies in 60 seconds is the same as how many copies in 285 seconds.

$ \dfrac{24}{60} = \dfrac{x}{285} $

Use cross multiplication to solve the equation.

$60x = 24 \cdot 285$

$60x = 6840$

$x = \dfrac{6840}{60} = 114$

The machine can make 114 copies in 4 minutes and 45 seconds.

mathstudent55 · Answer

Another way to solve this problem is to convert 4 minutes and 45 secionds into minutes. Since there are 60 secionds in 1 minute, 45 seconds = 45/60 minutes = 0.75 minutes.

This means that 4 minutes and 45 seconds is 4.75 minutes.

We use a proportion again.

24 copies is to 1 minutes as how many copies are to 4.75 minutes?

$\dfrac{24}{1} = \dfrac{x}{4.75} $

$x = 4.75 \cdot 24$

x = 114

The machine can make 114 copies in 4 minutes and 45 seconds.