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 cc 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 find the correct tape diagram that represents the context of Kadeesha's computer repair costs, we can break down the total costs involved.

We have:

1. The technician worked for 4.25 hours, charging an hourly rate \( c \) for labor.
2. The cost of parts is given as $91.
3. The total cost is $367.25.

We can express the total cost as: \[ \text{Total Cost} = \text{Cost of Parts} + \text{Cost of Labor} \] \[ 367.25 = 91 + 4.25c \]

From this equation, we can observe that the cost for labor (represented by \( 4.25c \)) and the fixed cost for parts ($91) contribute to the total cost ($367.25).

Now let's analyze the provided tape diagram options:

• Option A:

  • Shows \( c \) for labor repeated 4.25 times, followed by the cost of parts (91), and it sums up to \( 302.25 \). This doesn't correctly represent the total cost.

• Option B:

  • Shows the cost of parts repeated (91) and the labor \( c \) but does not correspond with the total cost or labor length.

• Option C:

  • Shows \( c \) for labor repeated (4.25 times), includes the cost of parts (91) with a total represented as \( 367.25 \). This aligns with our understanding of the total cost.

• Option D:

  • Like option B, it repeats the cost for parts but misrepresents the labor cost.

Thus, the best tape diagram that represents the context is:

C