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Weekend Bike Repair: Find the Missing Rate

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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.

1.
A customer pays for replacement parts and 3 hours of labor. Let x be the labor charge per hour.
Customer Receipt
ChargeAmount ($)
Parts17
Labor: 3 hours3x
Total68

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

2.
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?
Question 2 options
3.
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

4.
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? $

5.
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?
Question 5 options

Connect Arithmetic and Algebra

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

6.
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.

7.
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?
Question 7 options
8.
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

9.
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?
Question 9 options
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?
Question 12 options
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.