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