Question

Jim and Pam are making small trinkets for their wedding. Jim can make 2 trinkets per minute, and Pam can make 3 trinkets per minute. If they worked a total of 120 minutes and created 280 trinkets, how many minutes did Jim work, and how many did Pam work?

Answer 1

Jim worked for 80 minutes and Pam worked for 40 minutes.

Step-by-step explanation:

To find out how many minutes Jim and Pam each worked, we can set up a system of equations. Let's use J to represent the number of minutes Jim worked and P to represent the number of minutes Pam worked.

We know that Jim can make 2 trinkets per minute and Pam can make 3 trinkets per minute. So the total number of trinkets made by Jim would be 2J and the total number of trinkets made by Pam would be 3P.

From the information given, we have the following two equations:

J + P = 120 (total minutes worked)

2J + 3P = 280 (total trinkets made)

We can solve these equations simultaneously using substitution or elimination. Let's use the elimination method.

Multiplying the first equation by 2, we get:

2J + 2P = 240

Subtracting the new equation from the second equation, we eliminate J:

2J + 3P - (2J + 2P) = 280 - 240

Simplifying, we get:

P = 40

Substituting this value of P back into the first equation, we can solve for J:

J + 40 = 120

J = 80

Therefore, Jim worked for 80 minutes and Pam worked for 40 minutes.