Testinar Grade 7 math

Writing Two-Step Equations from Word Problems

Students will build Grade 7 mastery of writing two-step equations from word problems using models, equations, and test-style reasoning.

CH05-01 Equations and Inequalities
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. Naomi buys \(3\) books at \($8\) each and a \($5\) bookmark. Let \(t\) be her total cost. Which equation models this situation?

    1. \(t=3+8+5\)
    2. \(t=3(8+5)\)
    3. \(t=3(8)+5\)
    4. \(t=3+8\times5\)

  2. A car rental company charges a base fee of \($45\) and then \($0.25\) per mile. Which equation represents the total cost \(C\) for \(m\) miles?

    1. \(C=45m+0.25\)
    2. \(C=0.25m+45\)
    3. \(C=45(m+0.25)\)
    4. \(C=(45+m)(0.25)\)

  3. A phone company charges \($20\) per month plus \($0.15\) for each text message over the limit. If Marcus pays \($35.60\) in a month, which equation could be used to find \(n\), the number of text messages over the limit?

    1. \(0.15n+20=35.60\)
    2. \(20n+0.15=35.60\)
    3. \(20+35.60=0.15n\)
    4. \(0.15+20n=35.60\)

  4. A delivery service charges an initial fee of \($8\) plus \($3\) per package. If the total charge is \($26\), which equation represents this, where \(p\) is the number of packages?

    1. \(8p+3=26\)
    2. \(3p+8=26\)
    3. \(3(p+8)=26\)
    4. \(8+26=3p\)

  5. Jenna joins a gym with a membership fee of \($50\) and monthly charges of \($25\). Let \(m\) represent the number of months. Which equation shows the total cost \(T\) including the membership fee?

    1. \(T=50m+25\)
    2. \(T=25(m+50)\)
    3. \(T=50+25m\)
    4. \(T=(50+25)m\)

  6. A plumber charges \($65\) for a service call and \($40\) per hour of work. The total bill was \($185\). Which equation helps find \(h\), the number of hours worked?

    1. \(40+65h=185\)
    2. \(65+40h=185\)
    3. \(65(h+40)=185\)
    4. \(40h=185+65\)

  7. A baker buys flour in \(5\)-pound bags at \($3\) per bag. She also buys yeast for \($2\). If she spends \($17\) total, which equation represents the number of bags \(b\) she bought?

    1. \(5b+3=17\)
    2. \(3+2b=17\)
    3. \(3b+2=17\)
    4. \(5(b+2)=17\)

  8. A skateboard costs \($85\), and safety gear costs \($12\) per item. Marcus buys a skateboard and \(4\) safety items. Which equation represents his total cost \(C\)?

    1. \(C=85+4+12\)
    2. \(C=4(85+12)\)
    3. \(C=85+4(12)\)
    4. \(C=(85+12)(4)\)
Teacher and parent reference

Answer key and explanations

  1. C. \(t=3(8)+5\)

    The books cost \(3\times8=$24\) and the bookmark adds \($5\), so \(t=3(8)+5=29\).

  2. B. \(C=0.25m+45\)

    The per-mile cost \(0.25m\) is added to the fixed base fee \($45\).

  3. A. \(0.15n+20=35.60\)

    Base charge is \($20\); each extra text adds \($0.15\). So \(0.15n+20=35.60\).

  4. B. \(3p+8=26\)

    Initial fee is \($8\); each package adds \($3\). Equation: \(3p+8=26\).

  5. C. \(T=50+25m\)

    The one-time membership is \($50\) plus \($25\) each month, so \(T=50+25m\).

  6. B. \(65+40h=185\)

    Service call is \($65\) plus \($40\) per hour. So \(65+40h=185\).

  7. C. \(3b+2=17\)

    Each bag costs \($3\) and yeast is \($2\). Equation: \(3b+2=17\).

  8. C. \(C=85+4(12)\)

    Skateboard is \($85\) and safety gear is \(4 \times $12=$48\). Total equation: \(C=85+4(12)=$85+$48=$133\).

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