Worksheet

Weekend Bike Repair: Find the Missing Rate

Solve two-step equations from a student-run bike business, interpret solutions, and compare algebraic and arithmetic methods.

Grade 7MathInteractive · Printable

Aligned to7.EE.B.4.a

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
14 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 7
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students model and solve repair-business problems with equations of the forms px + q = r and p(x + q) = r.
Students compare arithmetic calculations with algebraic steps and interpret solutions in context.

How to use

Have students show equation steps on separate paper. Discuss how each arithmetic operation undoes a part of the business record.

Curriculum

Common Core standard covered

7.EE.B.4.a

Solve word problems with equations like px + q = r and p(x + q) = r, and compare the algebra with an arithmetic solution.

Preview

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Name Date

Weekend Bike Repair: Find the Missing Rate

Model repair records and compare equation-solving methods.

Read the Repair Records

Imani and Theo run a weekend bike-repair business. Use each independent record to find the unknown.

A customer pays for replacement parts and 3 hours of labor. Let x be the labor charge per hour.

Customer Receipt
Charge	Amount ($)
Parts	17
Labor: 3 hours	3x
Total	68

Use 3x + 17 = 68. What is the hourly labor charge? $ per hour

For each of 7 bikes, the students charge x dollars for a safety check and $6 for chain cleaning. They collect $133. Which equation models the charges?

A. 6(x + 7) = 133
B. 7(x + 6) = 133
C. 7x = 133 + 7 × 6
D. 7x + 6 = 133

A repair takes 1/2 hour. The customer pays $21, including a $7 part. The equation (1/2)x + 7 = 21 models the bill, where x is the hourly labor charge.

What is the hourly labor charge? $ per hour

Five customers each pay the same price for a tube replacement. Each bill includes a tube costing x dollars and $8 in labor. Together, the five bills total $112.50.

Use 5(x + 8) = 112.50. What is the cost of one tube? $

Imani spends 12 minutes setting up, then x minutes on each of 4 brake checks. The work takes 84 minutes altogether. Which pair gives a correct equation and arithmetic calculation for x?

A. 4x + 12 = 84; x = 84 ÷ 4 − 12
B. 12x + 4 = 84; x = (84 − 4) ÷ 12
C. 4x + 12 = 84; x = (84 − 12) ÷ 4
D. 4(x + 12) = 84; x = 84 ÷ 4 − 12

Connect Arithmetic and Algebra

Pay attention to what each operation represents. A fee charged once is different from a fee charged for every repair.

The students collect $162 for 6 identical repairs. Each repair includes x dollars in labor and $9 in parts, so 6(x + 9) = 162. Select every calculation that correctly finds the labor charge for one repair.

162 ÷ 6 − 9(162 − 9) ÷ 6(162 − 6 × 9) ÷ 6162 ÷ (6 + 9)162 − 6 × 9

Theo models a group appointment with 8(x + 3) = 136. Here x is the adjustment time per bike, and 3 is the inspection time per bike, both in minutes. His first algebraic step is x + 3 = 17. What does 17 represent?

A. It is the combined adjustment and inspection time for one bike.
B. It is the combined inspection time for all eight bikes.
C. It is the adjustment time without inspection for one bike.
D. It is the combined adjustment time for all eight bikes.

The students earn $14 for each flat-tire repair and $23 from one separate adjustment job. They collect $149 altogether. An arithmetic solution is (149 − 23) ÷ 14.

In 14x + 23 = 149, what is x, the number of flat-tire repairs? repairs

A customer buys 4 identical services at x dollars each and uses one $10 coupon. The final bill is $62, so 4x − 10 = 62. Which calculation finds the price of one service before the coupon?

A. Calculate 62 ÷ 4 + 10.
B. Calculate (62 − 10) ÷ 4.
C. Calculate 62 ÷ (4 + 10).
D. Calculate (62 + 10) ÷ 4.

10.

Three identical wheel repairs cost $93 altogether. Each repair includes x dollars for labor and $11 for parts. Imani starts with 3(x + 11) = 93 and expands it to 3x + 33 = 93.

After subtracting 33 from both sides, 3x = . The labor charge per wheel is $ .

Use and Check the Solutions

Build a model from each record. Interpret the unknown before making a decision.

11.

The students have 110 minutes available. They reserve 20 minutes for cleanup. Each bike needs a 5-minute inspection and x minutes of repair work. They can finish exactly 6 bikes using all the available time.

Use 6(x + 5) = 110 − 20. How many minutes of repair work can they spend on each bike? minutes

12.

The students want $85 left after paying a $19 weekend space fee. They charge $13 per repair and have no other costs. Which plan earns exactly the desired amount after the fee?

A. Complete 8 repairs, using (85 + 19) ÷ 13.
B. Complete 9 repairs, using 85 ÷ 13 and adding 2.
C. Complete 5 repairs, using (85 − 19) ÷ 13.
D. Complete 7 repairs, using 85 ÷ 13 and rounding up.

13.

A customer paid $48 for two identical repair packages. Each package included a $6 part and the same labor charge. For a new appointment, the customer wants one package with the same labor charge but a $9 part instead.

What should the new package cost? $

14.

For a repair with 2 hours of labor and $15 in parts, the bill is $65. Let x be the hourly labor charge. Theo writes 2x + 15 = 65 and gets 2x = 50. He says, “The hourly labor charge is $50.” Explain what $50 actually represents. Finish the algebra, and show an arithmetic calculation that finds the hourly charge.