Assume that the number of defective basketballs produced is related by a linear equation to the total number produced.

Question

Suppose that 15 defective balls are produced in a lot of 200, and 21 defective balls are produced in a lot of 300. Find the number of defective balls produced in a lot of 425 balls.

Answer 1

y = number of defective balls

 

x = total number of balls

 

Assume y = mx + b

 

m = (21 - 15) / (300 - 200) = 0.06

 

y = 0.06x + b

 

15 = 0.06(200) + b

 

b = 3

 

y = 0.06x + 3

 

For x = 425,

 

y = 0.06(425) + 3 = 28.5

 

You could round this up to 29.

Answer 2

X = # of balls produced

Y = # of defective balls found

 

(200, 15)

(300,21)

 

The slope is M= (21-15)/(300-200) = 6/100 = 3/50

 

we expect 3/50 * 450 = 3*9 = 27 defective balls in the lot of X=450.

 

The true linear equation is y = Mx + b

 

That is we need the y intercept, where the line

crosses the y-axis when x=0.

However, in this case, when x=0, the can

be no defective balls if none are produced.

So the point (0,0) forces B=0

 

The linear model is y=(3/50)X 

Expect 27 defective balls.