Mike is putting together information packets to give to parents at an open house. He can put together 18 packets in 20 minutes. Which of the following proportions could be used to find how many minutes, \( m \), it will take Mike to put together 120 packets?

1) \(\frac{18}{20} = \frac{m}{120}\)

2) \(\frac{20}{60} = \frac{m}{120}\)

3) \(\frac{18}{20} = \frac{77}{120}\)

4) \(\frac{m}{60} = \frac{120}{18}\)

The correct proportion for how many minutes Mike needs to assemble 120 packets is 18/20 = 120/m. Option 1 provides the correct set-up for the problem, allowing for cross-multiplication to solve for m.

Explanation:

The correct proportion to use in order to find how many minutes, m, it will take Mike to put together 120 packets, given that he can put together 18 packets in 20 minutes, is:

18/20 = 120/m

When solving for m, you cross-multiply to find the value that satisfies the proportion. This results in m = (120 × 20) / 18, which simplifies to the number of minutes Mike will need to assemble 120 packets.

Option 1 is the correct proportion because it reflects the direct relationship between the number of packets and the time it takes to put them together. As the number of packets increases, the time needed to assemble them also increases proportionally.