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?
i) Define variables.
ii) Write system of equations and solve.
iii) Write a sentence that answers the question.

Answer 1

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

Step-by-step explanation:

To solve this problem, let's define variables:

Let j = minutes Jim worked

Let p = minutes Pam worked

According to the given information, Jim can make 2 trinkets per minute and Pam can make 3 trinkets per minute. The total time they worked is 120 minutes and they created 280 trinkets.

From this, we can write the following system of equations:

2j + 3p = 280 (equation 1)

j + p = 120 (equation 2)

To solve this system of equations, we can use the substitution method or the elimination method. Let's solve it using the elimination method:

Multiply equation 2 by 2: 2(j + p) = 2(120)

2j + 2p = 240 (equation 3)

Subtract equation 3 from equation 1 to eliminate j:

(2j + 3p) - (2j + 2p) = 280 - 240

p = 40

Substitute the value of p into equation 2:

j + 40 = 120

j = 80

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