Renee is choosing between two different plans to buy electronic books for her tablet.

Plan 1 costs $6 per month plus an additional $1 per book.

Plan 2 has no monthly fee but each book costs $2.50.

The system of equations graphed on the coordinate plane below shows the total monthly cost, y, for each plan, based on the number of books, x, Renee buys in one month.

Which value represents the number of books when the costs for the two plans are equal?

A. 

0

B. 

4

C. 

6

D. 

10

To find the number of books when the costs for the two plans are equal, we need to set up the equations based on the cost structures of each plan.

**Plan 1**:  
Total cost $ y_1 = 6 + 1x $  
This can be simplified to:  
\[ y_1 = 1x + 6 \]

**Plan 2**:  
Total cost $ y_2 = 2.5x $

To find the point where the costs are equal, set the equations equal to each other:  
\[ 1x + 6 = 2.5x \]

Now, solve for $ x $:
1. Rearrange the equation:  
   \[ 6 = 2.5x - 1x \]  
   \[ 6 = 1.5x \]

2. Divide both sides by 1.5:  
   \[ x = \frac{6}{1.5} = 4 \]

Thus, the number of books when the costs for the two plans are equal is $ 4 $.

**Answer: B. 4**

Would you like any further details or have any questions? Here are some related questions to consider:

1. How would the costs change if Renee bought more than 10 books?
2. What is the cost difference between the two plans for 5 books?
3. At what point do the costs for the two plans start to diverge?
4. If Plan 1 had a higher monthly fee, how would that affect the crossover point?
5. How does the cost of books in Plan 2 compare to the additional cost per book in Plan 1?

**Tip:** When comparing linear cost functions, finding the intersection point (where costs are equal) is a useful method to determine which plan is more economical based on usage.

Renee is choosing between two different plans to buy electronic books for her tablet.

Plan 1 costs $6 per month plus an additional $1 per book.

Plan 2 has no monthly fee but each book costs $2.50.

The system of equations graphed on the coordinate plane below shows the total monthly cost, y, for each plan, based on the number of books, x, Renee buys in one month.

Which value represents the number of books when the costs for the two plans are equal?

A. 0

B. 4

C. 6

D. 10

Explore how to compare two book purchase plans using linear equations. Learn to set up and solve the equations y1 = 1x + 6 and y2 = 2.5x to find when costs are equal. Perfect for Grades 7-8 students studying algebra and cost comparisons.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation