Question

4. You, Newton, and Descartes have

504 volunteer hours altogether. How
many hours do you volunteer?
Volunteer Hours
You
Newton
Descartes
2 times Newton's hours
?
3 times Newton's hours

Answer 1

You have 168 volunteer hours, calculated by setting Newton's hours as N, using the relationship that you volunteer for twice and Descartes for three times as much as Newton, and dividing the total hours of 504 by the sum of these coefficients.

Step-by-step explanation:

The student asks about a volunteer hours problem involving a total of 504 hours between three people. Let's let N represent Newton's volunteer hours. According to the problem, you volunteer twice the amount of Newton's hours, and Descartes volunteers three times Newton's hours. The equation representing the total number of volunteer hours is:

2N (Your hours) + N (Newton's hours) + 3N (Descartes' hours) = 504
To find Newton's hours, we combine the terms that represent volunteer hours and divide by the combined coefficient:
2N + N + 3N = 504
6N = 504
N = 504 / 6
N = 84
This means Newton has 84 volunteer hours.
To find your volunteer hours, we multiply Newton's hours by 2:
2 × 84 = 168
You have 168 volunteer hours.