Reza and James have started exercising together. When they started, Reza weighed 185 pounds and James weighed 180. After 10 week
s, Reza weighed less than James. Assume that the weight change for each man was about the same, on average, each week. Write an inequality for the problem and determine the constraints on the variables.
Inequality: Let x = pound/week weight loss by Reza y = pounds/week weight loss by James
Therefore, after 10 weeks the two will weigh as follows: Reza = 185 - 10x James = 180 - 10y
But, Reza is said to be weighing less than James after 10 weeks. Then, the inequality will be as follows: 185 - 10x < 180 - 10y
Determination of the constraints: Solving the inequality written above; 185 - 10x < 180 - 10y 185 - 180 < 10x - 10y 5 < 10(x-y) 0.5 < x - y
Therefore, 0.5 + y < x or x > 0.5 + y
It can be seen that, for Reza to weigh less than James after 10 week, the loss of weight by Reza must be more than half to the rate of weight loss by James.
