Question 230434: The profits of a company that produces auto parts can be represented by a linear function. If the company sells 25 parts its profits are $80 and if the company sells 40 parts its profits are $125. Find the number of parts sold if the profits were $305. If the profits were $905.
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! Let x=the number of parts sold
Let y =the profit
Find the slope of the linear equation by using the slope formula:
m=(y2-y1)/(x2-x1)
In this case, y2=$125, y1=$80. x2=40, x1=25.
m=($125-$80)/40-25= $45/15
m=$3/part
We need to find the y-intercept (or b).
y=mx+b
I can choose either point (40,125) or (25,80).
y=mx+b
125=3*40+b
125=120+b
125-120=b
5=b
The line's equation is:
y=3x+5
If profits are $305:
305=3x+5
300=3x
x=100
If profits are $305, 100 parts were sold.
If profits are $905:
905=3x+5
900=3x
x=300
If profits were $905, 300 parts were sold.
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