Testinar Grade 7 math

Finding the Constant of Proportionality

Students will build Grade 7 mastery of finding the constant of proportionality using models, equations, and test-style reasoning.

CH01-03 Ratios and Proportional Relationships
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. The cost \(c\) of buying \(n\) identical books is proportional to \(n\). If \(4\) books cost \($18\), what is the constant of proportionality (unit price per book)?

    1. \($2.50\)
    2. \($4.00\)
    3. \($14.00\)
    4. \($4.50\)

  2. A bike rental costs \($2.50\) per hour. If \(h\) is the number of hours and \(c\) is the total cost, what is the constant of proportionality in the equation \(c = kh\)?

    1. \(1.0\)
    2. \(0.40\)
    3. \($5.00\)
    4. \(2.5\)

  3. The table shows a proportional relationship between pounds of sugar (\(s\)) and the number of cookies baked (\(c\)). In the equation \(c = ks\), what is the constant of proportionality (\(k\))?

    Finding the Constant of Proportionality visual for G7-C01-T03-Q003
    1. \(8\)
    2. \(10\)
    3. \(15\)
    4. \(12\)

  4. Which equation represents a proportional relationship with a constant of proportionality of \(3\)?

    1. \(y = 3x + 2\)
    2. \(y = x + 3\)
    3. \(y = \frac{x}{3}\)
    4. \(y = 3x\)

  5. A car travels \(120\) miles in \(2\) hours at a constant speed. What is the constant of proportionality (miles per hour)?

    1. \(240\) mph
    2. \(90\) mph
    3. \(100\) mph
    4. \(60\) mph

  6. The table shows the relationship between gallons of paint (\(g\)) and square feet painted (\(p\)). What is the value of \(k\) in the equation \(p = kg\)?

    Finding the Constant of Proportionality visual for G7-C01-T03-Q006
    1. \(100\)
    2. \(800\)
    3. \(200\)
    4. \(400\)

  7. A recipe calls for \(3\) cups of flour to make \(12\) cookies. At this rate, what is the constant of proportionality (cups per cookie)?

    1. \(4.0\)
    2. \(0.75\)
    3. \(3.0\)
    4. \(0.25\)

  8. A streaming service charges a proportional rate. If \(8\) months of service costs \($96\), what is the constant of proportionality (cost per month)?

    1. \($8\)
    2. \($10\)
    3. \($16\)
    4. \($12\)
Teacher and parent reference

Answer key and explanations

  1. D. \($4.50\)

    The constant of proportionality is \(k=c/n=18/4=$4.50\) per book.

  2. D. \(2.5\)

    In the equation \(c = 2.5h\), the coefficient \(k = 2.5\) is the constant of proportionality (unit rate per hour).

  3. D. \(12\)

    Using any pair in \(c = ks\): \(k = c/s = 24/2 = 12\) cookies per pound of sugar.

  4. D. \(y = 3x\)

    A proportional relationship has the form \(y = kx\) with no constant term. Here \(k = 3\).

  5. D. \(60\) mph

    Speed is distance divided by time: \(k = 120/2 = 60\) miles per hour.

  6. D. \(400\)

    \(k = p/g = 400/1 = 400\) square feet per gallon.

  7. D. \(0.25\)

    \(k = \frac{\text{flour}}{\text{cookies}} = \frac{3}{12} = 0.25\) cups per cookie.

  8. D. \($12\)

    \(k = 96/8 = $12\) per month.

Free Testinar sample Reviewed November 6, 2026 testinar.com
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