Question

Johnny and David are saving money to purchase an Xbox that costs $200.

Answer 1

Answer:

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 = $\frac{125 - 75}{5 - 0}$

  = 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,     $\frac{40 - 0}{2 -0}$

                                   = $\frac{80 - 40}{4 -2}$

                                   = $\frac{120 - 80}{6 -4}$

                                   = $\frac{160 - 120}{8 -6}$

                                   = $\frac{200 - 160}{10 -8}$

                                   = 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.