Read the following description of a relationship:
Martha signed up for a gym membership 6 weeks after Ruben.
Let a represent the number of weeks Martha has been a member and b represent the number of weeks Ruben has been a member.
Complete the table using the equation b = a + 6.
a b
1
7
2
3 19
4
Answer (2)
To complete the table using the equation b = a + 6 , we find the values for b when substituting the corresponding values of a . The completed table shows: when Martha has been a member for 1 week, Ruben has been a member for 7 weeks, and similar calculations yield the correct values for 2, 3, and 4 weeks. The final pairs are (1, 7), (2, 8), (3, 9), and (4, 10).
;
Substitute a = 1 into b = a + 6 to find b = 7 .
Substitute a = 2 into b = a + 6 to find b = 8 .
Substitute a = 3 into b = a + 6 to find b = 9 .
Substitute a = 4 into b = a + 6 to find b = 10 .
The completed table values for b are: 7 , 8 , 9 , 10 .
Explanation
Understanding the Problem We are given the equation b = a + 6 , which describes the relationship between the number of weeks Martha has been a gym member ( a ) and the number of weeks Ruben has been a member ( b ). We need to complete the table by finding the values of b for the given values of a .
Calculating b for a=1 For a = 1 , we substitute this value into the equation b = a + 6 to find the corresponding value of b :
b = 1 + 6 = 7 So, when Martha has been a member for 1 week, Ruben has been a member for 7 weeks.
Calculating b for a=2 For a = 2 , we substitute this value into the equation b = a + 6 to find the corresponding value of b :
b = 2 + 6 = 8 So, when Martha has been a member for 2 weeks, Ruben has been a member for 8 weeks.
Calculating b for a=3 For a = 3 , we substitute this value into the equation b = a + 6 to find the corresponding value of b :
b = 3 + 6 = 9 So, when Martha has been a member for 3 weeks, Ruben has been a member for 9 weeks. Note that the table already has an incorrect value of 19 for this case.
Calculating b for a=4 For a = 4 , we substitute this value into the equation b = a + 6 to find the corresponding value of b :
b = 4 + 6 = 10 So, when Martha has been a member for 4 weeks, Ruben has been a member for 10 weeks.
Final Answer The completed table is: a b 1 7 2 8 3 9 4 10
Examples
Understanding relationships between variables is crucial in many real-life scenarios. For instance, if you're tracking the progress of two projects where one started later than the other, you can use a similar equation to determine how far along the second project is compared to the first at any given time. This type of problem also lays the foundation for understanding linear functions and their applications in modeling real-world situations, such as calculating distances, speeds, or costs based on a fixed relationship.
