5x + 20 = y 5x + 20 = 70 5x = 50 x = 10 Jack has a business mowing lawns and charges a flat fee of $20 per yard, plus an additional $5 an hour. He wants to make sure that he makes at least $70 doing yard work for a client with a very large yard. He sets up and solves the equation above. What does his solution of 10 mean? A) He needs to mow at least 10 yards. B) He needs to work for at least 10 days for this client. C) He needs to work at least 10 hours in the client's yard. D) He needs to charge and additional $10 an hour for this client.

C) He needs to work at least 10 hours in the client's yard. Let's take a look at the equation that Jack created and solved to see what interpretation works for it. "Jack has a business mowing lawns and charges a flat fee of $20 per yard, plus an additional $5 an hour." This would indicate an expression of 20 + 5x = y where x is the number of hours worked and y = amount charged. The problem continues with "He wants to make sure that he makes at least $70 doing yard work for a client with a very large yard.", giving us 20 + 5x = 70 Now looking at the equation that Jack setup, it's identical except that the terms "20" and "5x" are swapped. This is OK since addition is commutative, so the order doesn't matter. And if you look at Jack's solution, you can see that Jack solved for x. So x=10. Now you just need to look up what x is representing in the equation we made and that turns out to be how many hours worked for the extra $5 per hour. With that in mind, of the available 4 choices, only "C) He needs to work at least 10 hours in the client's yard." makes any sense.