Math Problem Statement

How much does it cost to download each additional photo?

Solution

From the image provided, Liz subscribes to an online stock photo service, which charges a one-time membership fee and a per-photo fee. The task is to determine how much it costs to download each additional photo.

To solve this, we calculate the rate of change (slope) using the data in the table:

Table:

  • 60 photos: $81.00
  • 75 photos: $98.25
  • 100 photos: $127.00
  • 130 photos: $161.50

Formula for slope:

Slope (rate per photo)=ΔCostΔNumber of Photos\text{Slope (rate per photo)} = \frac{\Delta \text{Cost}}{\Delta \text{Number of Photos}}

Steps:

  1. Pick two points, such as:

    • (60, 81) and (75, 98.25)
  2. Calculate the slope: Slope=98.25817560=17.2515=1.15\text{Slope} = \frac{98.25 - 81}{75 - 60} = \frac{17.25}{15} = 1.15

The cost to download each additional photo is $1.15.

Final Answer:

1.15 dollars per photo\boxed{1.15 \text{ dollars per photo}}

Would you like me to break down any other part of the solution or analyze further details?


Here are 5 related questions for practice:

  1. What is the total membership fee Liz pays if the per-photo fee is $1.15?
  2. How many photos could Liz download for a total cost of $200?
  3. If Liz only downloads 30 photos, what would her total cost be?
  4. How would the total cost change if the per-photo rate increased to $1.50?
  5. How could you write an equation for the total cost based on the number of photos downloaded?

Tip: The slope formula is essential for understanding rate problems and interpreting data from tables!

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Rate of Change
Slope

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grade 8