Jonas mows lawns in the summer. In the past three years he has averaged, 13, 6 and 12 lawns a week. What is the minimum number of lawns he must mow per week on average this summer in order to maintain an average of 10 lawns a week each summer?

To find the minimum number of lawns Jonas must mow on average this summer, we first need to calculate the total number of lawns he has mowed in the past three years and then determine how many lawns he must mow this year to maintain an average of 10 lawns per week over four summers.

1. Jonas has averaged 13, 6, and 12 lawns per week over the past three years. To find the total number of lawns he mowed over these three summers, we sum the weekly averages and multiply by the number of weeks in a summer (assuming a summer has 52 weeks for consistency):
   \[
   \text{Total lawns mowed over 3 summers} = (13 + 6 + 12) \times 52 = 31 \times 52 = 1612 \text{ lawns}
   \]

2. To maintain an average of 10 lawns per week over four summers, he needs to mow a total of:
   \[
   \text{Total lawns needed over 4 summers} = 10 \times 4 \times 52 = 2080 \text{ lawns}
   \]

3. The number of lawns Jonas must mow this summer is the difference between the total lawns needed and the lawns already mowed:
   \[
   \text{Lawns to mow this summer} = 2080 - 1612 = 468 \text{ lawns}
   \]

4. To find the average number of lawns per week this summer, we divide the total lawns needed by 52 weeks:
   \[
   \text{Average lawns per week this summer} = \frac{468}{52} = 9 \text{ lawns per week}
   \]

Thus, Jonas must mow an average of **9 lawns per week** this summer to maintain an average of 10 lawns per week over four summers.

Would you like more details or have any other questions?

Here are some related questions:
1. How would the calculation change if the summers were shorter?
2. What if Jonas had mowed more lawns in the first three years?
3. How can this method apply to calculating averages in other areas?
4. What is the effect of rounding on average calculations?
5. How can we use this method for different types of averages (e.g., weighted averages)?

**Tip**: Always break down complex problems step by step to make them easier to solve!

Learn how to calculate the minimum number of lawns Jonas must mow per week this summer to maintain an average of 10 lawns per week over four summers. This problem covers concepts of averages and arithmetic mean, using step-by-step calculations. Suitable for students in Grades 7-9.

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