Math Problem Statement

Which answer choice below correctly interprets the unit rate of the situation represented by the graph?

A.There are 4 ounces of sugar in a dozen cookies. B.There are 8 ounces of sugar in a dozen cookies. C.There are 16 ounces of sugar in three dozen cookies. D.There are 32 ounces of sugar in four dozen cookies.

Solution

To determine the correct unit rate interpretation, we'll need to interpret the information from the graph. Since you haven't provided the graph directly, I'll explain the approach you can take.

  1. Find the slope: In a graph where one variable (like sugar) depends on another (like the number of cookies), the slope represents the unit rate. The slope is the change in sugar (y-axis) divided by the change in cookies (x-axis).

    If the graph shows a straight line, calculate the slope as: slope=ΔsugarΔcookies\text{slope} = \frac{\Delta \text{sugar}}{\Delta \text{cookies}}

  2. Unit Rate: The slope tells you how much sugar is used per 1 cookie or per some unit of cookies.

Now, looking at your options:

  • A. There are 4 ounces of sugar in a dozen cookies.
  • B. There are 8 ounces of sugar in a dozen cookies.
  • C. There are 16 ounces of sugar in three dozen cookies.
  • D. There are 32 ounces of sugar in four dozen cookies.

If the graph shows a rate of 4 ounces per dozen cookies, you would choose A. If the rate shows 8 ounces per dozen cookies, B would be correct, and so on.

Can you provide the graph or any other information to help me pinpoint the exact interpretation?


Here are 5 questions you might find useful:

  1. What is the relationship between the number of cookies and the amount of sugar on the graph?
  2. Is the graph a straight line or does it curve?
  3. What are the x and y values at a few key points on the graph?
  4. How do you calculate the slope from the graph?
  5. How can the slope help in understanding real-life scenarios (like baking)?

Tip: When finding a unit rate from a graph, always pick two points on the line, calculate the change in both directions, and divide the change in sugar by the change in cookies to get the rate.

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Math Problem Analysis

Mathematical Concepts

Unit Rate
Slope
Ratio and Proportion
Linear Equations

Formulas

Slope formula: m = Δy / Δx
Unit rate: rate = quantity1 / quantity2

Theorems

Concept of Proportionality
Linear Relationship Theorem

Suitable Grade Level

Grades 6-8