Final answer:
To find the number of sandwiches Jim makes, set j as the number of Jim's sandwiches, create the equation j + 2j = 42 to represent the total sandwiches made by both, and solve for j to find that Jim made 14 sandwiches.
Step-by-step explanation:
To determine j, the number of sandwiches Jim makes, we can set up an equation. Let j represent the number of sandwiches that Jim makes. Since Ron makes 2 times as many sandwiches as Jim, Ron makes 2j sandwiches. Together, they make a total of 42 sandwiches. We represent this situation with the equation:
j + 2j = 42
This equation combines the number of sandwiches made by Jim and twice that number for the sandwiches made by Ron to equal the total of 42 sandwiches made. To solve for j, we add Jim's number of sandwiches and Ron's number of sandwiches together and set this sum equal to 42:
3j = 42
To find the value of j, you divide both sides of the equation by 3:
j = 42 / 3j = 14
So, Jim made 14 sandwiches for the party.