Kadeesha needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged her $91 for parts. The total was $367.25. Which tape diagram could be used to represent the context if c represents the cost of labor per hour?

Question

A
c
c
c
...
91
302.25
4.25c
B
91
91
91
...
c
302.25
91c
C
c
c
c
...
91
367.25
4.25c
D
91
91
91
...
c
367.25
91c
Answer
Multiple Choice Answers
AA
BB
CC
DD

Answer 1

To represent the context of Kadeesha's computer repair costs using a tape diagram, we need to break down her total cost into the components it consists of: the labor (which depends on the cost per hour, \( c \), multiplied by the number of hours worked) and the parts cost.

1. Total Cost: $367.25
2. Parts Cost: $91
3. Labor Cost: To find the labor cost, we use the formula: $$ \text{Labor Cost} = c \times \text{Hours Worked} = 4.25c $$.

Now, we can see that:

• The total cost is the sum of parts and labor.

Thus, the equation we have looks like this: $$ 4.25c + 91 = 367.25 $$

This shows that:

• $91 is the cost for parts,
• $4.25c is the labor cost.

In terms of a tape diagram, we want to represent this sum appropriately:

• "4.25c" should occupy a length representing the labor cost,
• "91" should represent the parts cost, and
• the total should sum to 367.25.

Looking through the answer options:

• Option A consists of four lengths of "c" (for 4.25 hours, showing different segments of c) and then has one segment of 91 indicating the parts cost, and ends with the total of 367.25 which makes sense in structure.

The correct answer is A:

• Option A:
  • \( c \) (x4 for 4.25 hours of labor)
  • \( 91 \) for the parts cost
  • \( 302.25 \) which represents the remaining labor cost
  • \( 4.25c \) correctly represents it as a labor cost function.

So, the correct answer is A.