Testinar Grade 7 math

Writing Equations for Proportional Relationships

Students will build Grade 7 mastery of writing equations for proportional relationships using models, equations, and test-style reasoning.

CH01-04 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. A car travels at a constant speed of \(55\) miles per hour. Which equation relates distance \(d\) (miles) to time \(t\) (hours)?

    1. \(d=t+55\)
    2. \(d=\frac{t}{55}\)
    3. \(d=\frac{55}{t}\)
    4. \(d=55t\)

  2. A recipe calls for \(2\) cups of flour for every \(3\) cups of sugar. If \(f\) is flour and \(s\) is sugar, which equation shows this proportional relationship?

    1. \(f=\frac{3}{2}s\)
    2. \(f=s+1\)
    3. \(f=2s+3\)
    4. \(f=\frac{2}{3}s\)

  3. A store charges $4 per pound for apples. Which equation gives the total cost \(c\) (dollars) for \(p\) pounds?

    1. \(c=p+4\)
    2. \(c=\frac{4}{p}\)
    3. \(p=4c\)
    4. \(c=4p\)

  4. Maya runs at \(8\) miles per hour. After running for \(t\) hours, she has covered \(d\) miles. Which equation is correct?

    1. \(d=8+t\)
    2. \(d=\frac{8}{t}\)
    3. \(t=8d\)
    4. \(d=8t\)

  5. A phone plan charges $0.10 per minute. If \(m\) is the number of minutes and \(c\) is the cost in dollars, which equation models this?

    1. \(c=10m\)
    2. \(c=m+0.10\)
    3. \(m=0.10c\)
    4. \(c=0.10m\)

  6. A machine prints \(120\) pages every \(2\) minutes. What is the constant of proportionality \(k\) if \(p\) is pages and \(t\) is time in minutes?

    1. \(k=2\)
    2. \(k=120\)
    3. \(k=\frac{1}{60}\)
    4. \(k=60\)

  7. A photo costs $0.50 each. If you buy \(n\) photos for a total cost of \(T\) dollars, which equation is correct?

    1. \(n=0.50T\)
    2. \(T=n+0.50\)
    3. \(T=\frac{0.50}{n}\)
    4. \(T=0.50n\)

  8. The table shows the relationship between gallons of gas and cost. Which equation represents this relationship?

    Writing Equations for Proportional Relationships visual for G7-C01-T04-Q009
    1. \(C=3g+1\)
    2. \(C=\frac{g}{4}\)
    3. \(C=g+9\)
    4. \(C=4g\)
Teacher and parent reference

Answer key and explanations

  1. D. \(d=55t\)

    For a proportional relationship, \(d=kt\) where \(k\) is the constant of proportionality. Here \(k=55\).

  2. D. \(f=\frac{2}{3}s\)

    The ratio flour:sugar is \(2:3\), so \(f=\frac{2}{3}s\) where the constant of proportionality is \(\frac{2}{3}\).

  3. D. \(c=4p\)

    Cost is price times quantity. The constant \(k=4\) dollars per pound, so \(c=4p\).

  4. D. \(d=8t\)

    Distance equals speed times time. With speed \(k=8\) mph, the equation is \(d=8t\).

  5. D. \(c=0.10m\)

    The constant of proportionality is $0.10 per minute, so \(c=0.10m\).

  6. D. \(k=60\)

    The rate is \(\frac{120 \text{ pages}}{2 \text{ minutes}}=60\) pages per minute, so \(k=60\).

  7. D. \(T=0.50n\)

    Cost equals price per item times number of items. Here \(T=0.50n\).

  8. D. \(C=4g\)

    The ratio is \(\frac{12}{3}=4\), \(\frac{20}{5}=4\), \(\frac{32}{8}=4\). The equation is \(C=4g\).

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