Math 7B. Pattering and Algebraic Reasoning. Spring25 Sample work

Question 2
Luca rode his bicycle 8 kilometers on Monday. On Tuesday, he rode his bicycle 20% farther than he rode on Monday. On Wednesday, he rode his bicycle 10% farther that he rode on Tuesday.
Complete the following prompts.
***Do not round the numbers***
How many more kilometers did Luca ride his bicycle on Tuesday?_____ kilometers
How far did Luca ride his bicycle on Tuesday?_____ kilometers
How many more kilometers did Luca ride his bicycle on Wednesday?_____ kilometers
How far did Luca ride his bicycle on Wednesday?
8.3 kilometers
9.68 kilometers
10.4 kilometers
or 10.56 kilometers

1 answer

To solve the problem, let's start with the information given:

  1. Monday's distance: Luca rode 8 kilometers.

  2. Tuesday's distance: He rode 20% farther than Monday.

    To calculate Tuesday's distance:

    • Increase on Tuesday = 20% of 8 kilometers \[ 20% \text{ of } 8 = 0.20 \times 8 = 1.6 \text{ kilometers} \]
    • Therefore, distance on Tuesday = Monday's distance + Increase on Tuesday \[ \text{Tuesday's distance} = 8 + 1.6 = 9.6 \text{ kilometers} \]
  3. Wednesday's distance: He rode 10% farther than Tuesday.

    To calculate Wednesday's distance:

    • Increase on Wednesday = 10% of Tuesday's distance \[ 10% \text{ of } 9.6 = 0.10 \times 9.6 = 0.96 \text{ kilometers} \]
    • Therefore, distance on Wednesday = Tuesday's distance + Increase on Wednesday \[ \text{Wednesday's distance} = 9.6 + 0.96 = 10.56 \text{ kilometers} \]

Now, let's answer the prompts.

  1. How many more kilometers did Luca ride on Tuesday compared to Monday?

    • Distance on Tuesday - Distance on Monday = 9.6 - 8 \[ \text{More on Tuesday} = 1.6 \text{ kilometers} \]
  2. How far did Luca ride his bicycle on Tuesday?

    • Distance on Tuesday = 9.6 kilometers.
  3. How many more kilometers did Luca ride on Wednesday compared to Tuesday?

    • Distance on Wednesday - Distance on Tuesday = 10.56 - 9.6 \[ \text{More on Wednesday} = 0.96 \text{ kilometers} \]
  4. How far did Luca ride his bicycle on Wednesday?

    • Distance on Wednesday = 10.56 kilometers.

So, the answers are:

  • How many more kilometers did Luca ride his bicycle on Tuesday? 1.6 kilometers
  • How far did Luca ride his bicycle on Tuesday? 9.6 kilometers
  • How many more kilometers did Luca ride his bicycle on Wednesday? 0.96 kilometers
  • How far did Luca ride his bicycle on Wednesday? 10.56 kilometers

Thus, the final answers are:

  • 1.6 kilometers
  • 9.6 kilometers
  • 0.96 kilometers
  • 10.56 kilometers