You can buy t-shirts for 12$ each, polo shirts for 24$, and rugby shirts for 36$ each. suppose you want to have the same number of t-shirts as polo shirts. buying 200 shirts with a budget of $5400, how many of each shirt should you buy?

50 t-shirts, 50 polo shirts, 100 rugby shirts

Step-by-step explanation:

1) same number of T-shirts as polo shirts

  x (t- shirts) and x (polo shirts) = x + x

2) y rugby shirts

3) x+x+y = 200 shirts

  2x + y = 200

4) 12x + 24x + 36y = 5400

   36x + 36y = 5400

   36(x+y) = 5400

    x + y = 150

5) 2x + y = 200

 -   ( x + y = 150)

      x         = 50

6) 2x+y = 200

   2*50 + y = 200

  100 + y = 200

          y =100

7) check

12x + 24x + 36y = 5400

12*50 + 24*50 + 36 * 100 = 5400

5400 = 5400

1. perpendicular

2. parallel

3. perpendicular

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.