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?

a. 10 weeks

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

c. 220 kg.

Step-by-step 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)

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.