Q:

In 2010, josie and salvador each worker an eight-hour days each week, How many weeks did it take josie to earn $ 1,000 more than salvador.

Accepted Solution

A:
the complete question in the attached figure

step 1
find the equation of the line Josie’s and Salvador’s wages

Josie’s  wages
we have 
the points (3,26.25)  and (5,43.75)
slope m=(43.75-26.25)/(5-3)------> m=8.75
with m and the point (3,26.25)
y-y1=m*(x-x1)------> y-26.25=8.75*(x-3)---> y=8.75x-26.25+26.25
y=8.75x------> equation 1

Salvador’s wages
we have 
the points (2,15)  and (6,45)
slope m=(45-15)/(6-2)------> m=7.5
with m and the point (2,15)
y-y1=m*(x-x1)------> y-15=7.5*(x-2)---> y=7.5x-15+15
y=7.5x------> equation 2

step 2
 the difference equation 1 and equation 2 must be $1000
so
8.75x-7.5x=1000-------> 1.25x=1000------> x=1000/1.25
x=800 hours
Josie and Salvador each worked an eight-hour day for five days each week
so
each week is 8*5-------> 40 hours

if 1 week is-----------> 40 hours
  X-----------------> 800 hours
x=800/40-----> x=20 weeks

the answer is
20 weeks