Johnny and david are saving money to purchase an xbox that costs $200.

a. which function (s) are linear?

b. which function (s) are proportional?

c. write an equation for johnny

d. write an equation for david

e. who is able to purchase their xbox first? how do you know?

A. Both of Johny's (f(x)) and David's functions (g(x))  are linear.

B. (f(x) - 75) ∝ x and  g(x) ∝ x

where x = no. of working hours,

          f(x), g(x)  = money saved

C. Equation for Johny is,

  y = 75 + 10x

where, x = no. of hours Johny works

            y = money saved by Johny.

D. Equation for David is,

  y = 20x

where, x = no. of hours David works

            y = money saved by David

E. David will buy the X-box earlier. it can be found by putting f(x) = g(x) = 200 in the two equations and from that comparing the two values of x.

Step-by-step explanation:

Let the equation for Johny be,

y = mx + c

where c is the y intercept which is here 75 and m is the slope of the straight line which is here ,

m =

  = 10      [since (125 ,5) and (75 ,0) are over the straight line]

So, Johny's equation is,

y = 10x + 75 = f(x) [say]-------------------------------------------------(1)

which is linear.

Now slopes of different straight lines connecting the points for David  are all equal to 20 ,

                      [since,    

                                   =

                                   =

                                   =

                                   =

                                   = 20]

So, David's equation is also a straight line with y intercept 0 and slope 20.

So, David's equation is,

y = 20x = g(x) [say] --------------------------(2)

A. Now, from (1) and (2) both of Johny's and David's functions  are linear.

B. From (1)  (f(x) - 75) ∝ x and from (2)  g(x) ∝ x

C. Equation for Johny is,

  y = 75 + 10x

where, x = no. of hours Johny works

            y = money saved by Johny.

D. Equation for David is,

  y = 20x

where, x = no. of hours David works

            y = money saved by David

E. Putting y = 200 in (1) we  get,

125 = 10x

⇒12.5 , so, Johny will earn the money in 12.5 hours.

and, putting y = 200 in (2) we get, x = 10 so, David will earn the money in 10 hours. since, 10 < 12.5 so, David will be able to purchase the X-box first.

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