Math Problem Statement

Which of the following situations best matches the data in the table?

Solution

The table shows a set of values for xx and yy, where xx could represent time (e.g., days, months) and yy represents some quantity that changes over time.

The data in the table is:

xxyy
08
19.5
211
312.5

Let's break down the given options and analyze which one matches this dataThe table shows a set of values for xx and yy, where xx could represent time (e.g., days, months) and yy represents some quantity that changes over time.

The data in the table is:

xxyy
08
19.5
211
312.5

Let's break down the given options and analyze which one matches this

Option A:

"Robbie has $8 in his account and spends $1.50 each day for the next 3 days."

  • At x=0x = 0 (day 0), Robbie has $8.
  • Each day, he spends $1.50, so after 1 day (when x=1x = 1), he would have 81.50=6.508 - 1.50 = 6.50, and this does not match the value of y=9.5y = 9.5 in the table. This option does not fit.

Option B:

"Zach sells t-shirts for $9.50 each."

  • This doesn't involve any specific rate of change over time or relate to the given xx and yy data. So, this option does not match.

Option C:

"A newborn weighs 8 pounds at birth and gains 1.5 pounds each month for the next 3 months."

  • At x=0x = 0 (birth), the weight is 8 pounds.
  • After 1 month (x=1x = 1), the baby gains 1.5 pounds, making the weight 8+1.5=9.58 + 1.5 = 9.5 pounds.
  • After 2 months (x=2x = 2), the baby weighs 9.5+1.5=119.5 + 1.5 = 11 pounds.
  • After 3 months (x=3x = 3), the baby weighs 11+1.5=12.511 + 1.5 = 12.5 pounds.

This matches perfectly with the data in the table.

Option D:

"Riley earns $8 an hour lifeguarding, plus $1.50 for any pool memberships she sells."

  • This suggests a linear relationship, but the numbers do not correspond to the data in the table, as Riley's earnings don't match the values of yy based on the table’s xx.

Conclusion:

The situation that best matches the data in the table is Option C, where the newborn weighs 8 pounds at birth and gains 1.5 pounds each month for the next 3 months.

Would you like more details on this solution or have any further questions?

Here are 5 related questions to expand on this problem:

  1. How would the equation of this linear relationship between xx and yy be written?
  2. If the newborn continued gaining weight at the same rate, what would its weight be at 6 months?
  3. How can we represent the situation in a graph and what would the slope represent?
  4. How can you check whether a situation represents a linear function?
  5. How does the rate of change affect the interpretation of real-world problems?

Tip: In problems involving linear relationships, always check for a constant rate of change by comparing differences in yy values as xx increases.

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Rate of Change

Formulas

y = mx + b

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-8