Answer:
To solve this problem we can construct an linear algebraic expression for each person, principally denoted as:
where
y :is our dependent variable (which is a function of )
x :is our independent variable
a :is the slope
c :is the y-intercept constant value (if any present)
Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.
Tamara
Has already made 20 widgets and produces at a rate of 8 widgets per hour thus here c=20 and a=8 , so Tamara's equation reads: yT=8x+20
Jason
Has not produced any widgets yet and produces at a rate of 12 widgets per hour thus here c=0 and a=12 , so Jason's equation reads:yj=12x
So the system of equations will be
yT=8x+20
yj=12x
Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?
Since we want to find the amount of time (i.e. the value of x ) it takes for both of them to produce the same number of widgets we can just equate the two equations ans solve for x as follow:
yT=yj
8x+20=12x
8x-12x=-20
-4x=-20
x=5
So it takes them 5 hours to produce the same amount of widgets
Part C: How many widgets will Tamara and Jason have produced?
Now we can simply plug in the value of x=5 in any of the two equations (i.e. either for Tamara or Jason) to find the number of widgets produced.
yT=8(5)+20=40+20=60
So in a time-space of 5 hours Each will have produced 60 widgets and in total will be 60+60 = 120 widgets.
Step-by-step explanation:
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