Read the following description of a relationship:
Tessa is determined to become a concert pianist. Every week she practices more hours than her piano teacher assigns.
Let [tex]$a$[/tex] represent the number of hours of practice assigned and [tex]$c$[/tex] represent the number of hours of practice completed.
Complete the table using the equation [tex]$c=a+8$[/tex].
a c
1 $\square$
2 10
3 11
4
Answer (1)
Substitute a = 1 into the equation c = a + 8 to find c .
Calculate c = 1 + 8 = 9 .
Substitute a = 4 into the equation c = a + 8 to find c .
Calculate c = 4 + 8 = 12 . The missing values are 9 , 12 .
Explanation
Understanding the Problem We are given the equation c = a + 8 , which relates the number of hours of practice assigned ( a ) to the number of hours of practice completed ( c ). We need to complete the table by finding the values of c for the given values of a .
Calculating c when a=1 When a = 1 , we substitute this value into the equation to find the corresponding value of c :
c = 1 + 8 = 9 So, when a = 1 , c = 9 .
Calculating c when a=4 When a = 4 , we substitute this value into the equation to find the corresponding value of c :
c = 4 + 8 = 12 So, when a = 4 , c = 12 .
Final Answer Therefore, the completed table is:
a
c
1
9
2
10
3
11
4
12
The missing values are 9 and 12 .
Examples
Understanding relationships between variables with simple equations is crucial in many real-life scenarios. For instance, if you are tracking your expenses, you might have a fixed cost (like a subscription) and a variable cost (like usage). If your monthly subscription to a streaming service is $8 and you pay 1 f ore v ery m o v i eyo u re n t , t h e t o t a l cos t c c anb ere p rese n t e d a s c = a + 8 , w h ere a$ is the number of movies you rent. By understanding this equation, you can easily calculate your total monthly expenses based on the number of movies you watch.
