Question 230450
What the problem is really asking is:
What is the straight line equation that goes
through the points (400,9) and (525,19)?
Then find the point on the line (x,y)
where {{{y}}} is unknown, and {{{x = 700}}}
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I'll use the equation
{{{(y - y[1])/(x - x[1]) = (y[2] - y[1])/(x[2] - x[1])}}}
where
{{{x[1] = 400}}}
{{{y[1] = 9}}}
and
{{{x[2] = 525}}}
{{{y[2] = 19}}}

{{{(y - 9)/(x - 400) = (19 - 9)/(525 - 400)}}}
{{{(y - 9)/(x - 400) = 10/125}}}
{{{125*(y - 9) = 10*(x - 400)}}}
{{{125y - 1125 = 10x - 4000}}}
{{{125y = 10x - 2875}}}
{{{25y = 2x - 575}}}
{{{y = (2/25)*x - 23}}}
Now I can find (700,y)
{{{y = (2/25)*700 - 23}}}
{{{y = 56 - 23}}}
{{{y = 33}}}
There will be 33 defective balls in a lot of 700
check answer:
{{{y = (2/25)*x - 23}}}
{{{9 = (2/25)*400 - 23}}}
{{{9 = 32 - 23}}}
{{{y = 9}}}
OK
{{{y = (2/25)*x - 23}}}
{{{y = (2/25)*525 - 23}}}
{{{y = 42 - 23}}}
{{{y = 19}}}
OK