A copy machine makes 78 copies in 3 minutes and 15 seconds . How many copies does it make per minute.

Answer 1

Hi, Brook! I think I can help you with this one.

1) Simplifying minutes + seconds to just seconds

Let's start with turning 3 minutes and 15 seconds into one unit of time.

To do this, we have to realize that 1 minute = 60 seconds, and 3 minutes is 180 seconds (3 minutes x 60 seconds each = 180 seconds total). Let's add 15 to 180 (because we're working with 3 minutes and 15 seconds) to give us 195 seconds total.

The information that we have now is that a copy machine makes 78 copies in 195 seconds.

2) Writing a proportion

Let's write a proportion to solve the question "How many copies does the machine make per minute?"

78 copies/195 seconds = x copies/60 seconds

The numerators (the number on top of the fraction) on both sides represent the number of copies, and the denominators (the number on the bottom of the fraction) on both sides represent the amount of seconds it takes to print the given number of copies. Since we want to know how many copies are produced in 60 seconds (or 1 minute), the unknown number of copies can be written as the variable x.

3) Solving the equation

To solve, we can cross-multiply. This means taking a numerator and multiplying it by the denominator of the other fraction, then doing the same for the other numerator and denominator. The products should be equivalent. Let's visualize this:

78 (numerator of fraction #1) times 60 (denominator of fraction #2) = 4680

x (numerator of fraction #2) times 195 (denominator of fraction #1) = 195x

Since the products have to be the same, we can say that 195x = 4680.

To solve for x, we can divide both sides by 195 in order to isolate x. The result will leave you with the amount of copies the machine can make in 1 minute.

Hope this helps!