To arrive at the answer, I graphed the piecewise function using a graphing calculator, then evaluated it at x=38 and x=52. I drew a line at y=445 and found the point of intersection on the graph.
a) The difference between earnings for 52 hours ($580) and earnings for 38 hours ($380) is
$200.
b) An employee must work
43 hours to earn $445.
Let x be the earnings/hour at the movie theater.
y be the earnings/hour at the pet store
Systems of equations:
$152.50 = 10x + 8y
$171 = 8x + 10y
Solving for x and y:
x = $4.36/ hour in the movie theater
y = $13.61/ hour in the pet store.<span />
Given that the line passes through points:
(2,6), (1,3)
the equation will be given by:
m(x-x1)=y-y1
where
slope, m=(y-y1)/(x-x1)
from the points given:
m=(6-3)/(2-1)=3/1=3
thus the equation will be given by:
using point (1,3)
3(x-1)=y-3
3x-3=y-3
hence
y=3x-3+3
y=3x
Answer: y=3x
In order to make this easier, let us convert the fraction into a mixed number. 2 2/3 would become 8/3. Now, let us divide 8 pints by 8/3 cups and we get 24/8 or 3 cups. Therefore, the amount of water that Cary has to use when she makes barbecue sauce with 1 pint of tomato is 3 cups.
