Testinar Grade 6 math

Two Quantities That Change Together

Students will build Grade 6 mastery of two quantities that change together using models, equations, and test-style reasoning.

CH03-10 Expressions and Equations
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A worker earns \($15\) per hour. Which equation relates total earnings \(E\) to hours worked \(h\)?

    1. \(E=15+h\)
    2. \(E=15h\)
    3. \(E=\frac{15}{h}\)
    4. \(E=h-15\)

  2. A car travels at a constant speed of \(60\) miles per hour. Which variable is independent?

    1. Distance traveled
    2. Time driven
    3. Speed of the car
    4. Fuel consumption

  3. The table below shows the relationship between the number of pizzas ordered and the total cost. What is the rule that relates cost \(C\) to the number of pizzas \(p\)?

    Two Quantities That Change Together visual for G6-C03-T10-Q003
    1. \(C = 8p\)
    2. \(C = 12p\)
    3. \(C = 10p\)
    4. \(C = 9p\)

  4. The distance \(d\) (in miles) traveled by a cyclist is related to time \(t\) (in hours) by the equation \(d = 20t\). What does the number \(20\) represent in this context?

    1. The cyclist's speed in miles per hour
    2. The distance traveled
    3. The time in hours
    4. The total hours of cycling

  5. A table shows the cost of buying notebooks. Which equation best represents this relationship?

    Two Quantities That Change Together visual for G6-C03-T10-Q005
    1. \(\text{Cost} = 2 \times \text{Notebooks}\)
    2. \(\text{Cost} = 3 \times \text{Notebooks}\)
    3. \(\text{Cost} = \text{Notebooks} + 1\)
    4. \(\text{Cost} = 2 \times \text{Notebooks} + 1\)

  6. A gym membership costs \($50\) per month. If \(m\) represents the number of months and \(T\) represents the total cost, which equation is correct?

    1. \(m = 50T\)
    2. \(T = 50 + m\)
    3. \(T = 50m\)
    4. \(T = m - 50\)

  7. The graph below shows the relationship between the number of hours worked and earnings. Based on the graph, how much does an employee earn per hour?

    Two Quantities That Change Together visual for G6-C03-T10-Q007
    1. $\(2\) per hour
    2. $\(3\) per hour
    3. $\(4\) per hour
    4. $\(5\) per hour

  8. A store charges \($3\) per item. Complete the table. What are the missing costs?

    Two Quantities That Change Together visual for G6-C03-T10-Q009
    1. $\(12\) and $\(30\)
    2. $\(15\) and $\(36\)
    3. $\(18\) and $\(48\)
    4. $\(24\) and $\(60\)
Teacher and parent reference

Answer key and explanations

  1. B. \(E=15h\)

    Earnings equal hourly rate multiplied by hours worked: \(E=15h\).

  2. B. Time driven

    The independent variable is what you control or choose. Time is chosen first; distance depends on time.

  3. D. \(C = 9p\)

    Each pizza costs $\(9\). Check: when \(p=2\), \(C=9(2)=18\); when \(p=4\), \(C=9(4)=36\). The rule is \(C=9p\).

  4. A. The cyclist's speed in miles per hour

    In the equation \(d=20t\), \(20\) is the constant rate of change (the speed), and \(t\) is the time.

  5. A. \(\text{Cost} = 2 \times \text{Notebooks}\)

    The cost is $\(2\) per notebook. Check: \(1\) notebook costs $\(2\); \(3\) notebooks cost \($6\). The equation is \(\text{Cost}=2n\).

  6. C. \(T = 50m\)

    Total cost equals $\(50\) per month times the number of months: \(T=50m\).

  7. A. $\(2\) per hour

    The graph shows the line passes through \((2,4)\) and \((4,8)\). The slope is \(\frac{8-4}{4-2}=\frac{4}{2}=2\), so the rate is $\(2\) per hour.

  8. B. $\(15\) and $\(36\)

    At $\(3\) per item: \(5\) items cost \(3 \times 5 = 15\) dollars; \(12\) items cost \(3 \times 12 = 36\) dollars.

Free Testinar sample Reviewed November 6, 2026 testinar.com
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