Question

Sam is trying to lose weight, and George is trying to gain weight. Sam’s weight in pounds can be represented by the function f(x) = 240 – 2x, where x is the number of weeks since Sam started losing weight. George’s weight in pounds can be represented by the function g(x) = 180 + 4x, where x is the number of weeks since George starting gaining weight.

a. What is the x-value when f(x) = g(x)


b. When f(x) = g(x), what does the x-value represent?


c. When Sam and George weigh the same, what will their weight be?

Answer 1

a. 10 weeks

b. 10 weeks is the time after which Sam and George will have the same weight.

c. 220 kg.

Explanation:

Sam is trying to lose weight at the rate of 2 kg per week from his original weight of 240 kg.

So, f(x) = 240-2x ....... (1), where x is the number of weeks and f(x) is his weight after x weeks.

Again, George is trying to gain weight at the rate of 4 kg per week from his original weight of 180 kg.

So, g(x) = 180+4x, where x is the number of weeks and g(x) is his weight after x weeks.

a. When f(x) =g(x) , then 240-2x = 180+4x

⇒ 6x = 60

⇒ x =10 weeks.

b. when f(x) =g(x), then the value of x i.e. 10 weeks is the time after which Sam and George will have the same weight.

c. At x= 10, from equation (1), f(x) = 240-2(10) =220 kg.

This 220 kg weight is the same for Sam and George after 10 weeks. (Answer)