Question

Kari worked twice as many hours as Chris. She also worked ten less than three times as many hours as Mark. Chris and Mark worked the same number of hours. Let H be the number of hours Chris worked. How many hours did Mark work?

A) Mark worked 2H hours.
B) Mark worked 3H hours.
C) Mark worked 2H - 10 hours.
D) Mark worked 3H - 10 hours.

Answer 1

The number of hours Mark worked is represented by H, which is the same number of hours as Chris. The algebraic expressions equate Kari's hours based on Chris's (2H) to Kari's hours based on Mark's (3H - 10), confirming that Chris and Mark worked the same number of hours.

Step-by-step explanation:

In solving this problem, we need to convert the given information into algebraic expressions. The problem states that Kari worked twice as many hours as Chris and ten less than three times as many hours as Mark. Since Chris and Mark worked the same number of hours, we let H represent the number of hours worked by Chris and consequently by Mark. If we express Kari's hours based on Chris's hours, it would be 2H. Then, if we express Kari's hours based on Mark's hours, it would be 3H - 10. Since both expressions describe the hours Kari worked and Chris and Mark worked the same number of hours, we can equate them to each other:

2H = 3H - 10

Now, since the question is about how many hours Mark worked, we already established that Mark worked H hours, which is the same as Chris. Therefore, the answer to the question "How many hours did Mark work?" would be that Mark worked H hours.