Question

Reza and James have started exercising together. When they started, Reza weighed 185 pounds and James weighed 180. After 10 weeks, 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.

Answer 1

0.5 + y < x or x > 0.5 + y

Explanation:

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.

Answer 2

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.