Explanation:
Let’s define the variables:
Let’s represent the weight of Momo’s package as “m” (in pounds) and the weight of Tom’s package as “t” (in pounds).
Setting up the system of equations:
From the given information, we can write the following equations:
Equation 1: Tom’s package weights three more pounds than twice the weight of Momo’s package:
t = 2m + 3
Equation 2: The total weight of both packages is 15 pounds:
t + m = 15
Solving the system using substitution or elimination:
We can solve this system of equations using either substitution or elimination method. Let’s use the substitution method.
First, let’s solve Equation 1 for t:
t = 2m + 3
Now, substitute this value of t in Equation 2:
(2m + 3) + m = 15
Simplifying the equation:
3m + 3 = 15
Subtracting 3 from both sides:
3m = 12
Dividing both sides by 3:
m = 4
Now substitute the value of m back into Equation 1 to find t:
t = 2(4) + 3
t = 8 + 3
t = 11
Therefore, the weight of Momo’s package is 4 pounds, and the weight of Tom’s package is 11 pounds.
Justification:
From the information given, we established the equation t = 2m + 3 to represent the relationship between the weights of Tom’s package and Momo’s package.
And from the equation t + m = 15, we determined the total weight of both packages to be 15 pounds.
By solving the system of equations, we found the weight of Momo’s package to be 4 pounds and Tom’s package to be 11 pounds, which satisfies the given conditions.