Peggy wants to give piano lessons at her home. She has 10 students per week for a half-hour lesson, and 5 students per week for a full-hour lesson. Which expression below represents how many dollars she will earn per week at a rate of $10 per half-hour lesson and $16 per full-hour lesson?

1. 10(10)+ 5(10)
2. 10(16) + 5(10)
3. 10(10) + 5(16)
4. 10(16) + 5(8)

10(10)+ 5(10)

I'll be glad to check YOUR answer.

Right.

To find out how much Peggy will earn per week, we need to calculate the earnings for each type of lesson separately and then add them together.

For the half-hour lessons, she has 10 students per week, and each lesson costs $10. So the total earnings from the half-hour lessons can be calculated as 10 * 10.

For the full-hour lessons, she has 5 students per week for a full-hour lesson, and each lesson costs $16. So the total earnings from the full-hour lessons can be calculated as 5 * 16.

Now, let's look at the options provided:

1. 10(10) + 5(10): This expression represents earning $10 for a half-hour lesson and $10 for a full-hour lesson, which is incorrect.

2. 10(16) + 5(10): This expression represents earning $16 for a half-hour lesson and $10 for a full-hour lesson, which is incorrect.

3. 10(10) + 5(16): This expression represents earning $10 for a half-hour lesson and $16 for a full-hour lesson, which is correct.

4. 10(16) + 5(8): This expression represents earning $16 for a half-hour lesson and $8 for a full-hour lesson, which is incorrect.

Therefore, the correct expression representing Peggy's earnings per week would be 10(10) + 5(16).