Before treatment it was measured that there were .035 mg/ml cancer ....?

Question

Before treatment it was measured that there were .035 mg/ml cancer cells and .02 mg/ml white blood cells in a patient; and after treatment there were .05 mg/ml white blood cells and only .00875 mg/ml cancer

cells. Given a linear relationship, what was the original amount

of cancer cells?

Answer 1

Let the independent variable be mg/ mL of white blood cells within a patient. That is, they number of cancer cells is dependent on the number of white blood cells within the patient.

x: mg/ ml of white blood cells within a patient

y: mg/ ml of white blood cells within a patient

If we were to represent the information provided, we could say;

(x,y)

(0.02, 0.035)

(0.05,0 .00875)

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Given the function is a linear relation, we know that...

y - a= m (x - b)

... where 'm' is the gradient, 'a' is a y coordinate, 'b' is the corresponding x coordinate

We also know that the gradient can be found by...

(y2-y1) / (x2-x1)

... where x1 and y1 are one pair of coordinates, and x2 and y2 are another pair of coordinate

--------------------------------------...

y - 0.035= [(0.035 - 0.00875) / (0.02 - 0.05)] (x - 0.02)

y - 0.035= -0.875 (x - 0.02)

y= -0.875 x - 0.0175 + 0.035

y= 1.75 x + 0.0175

Assuming the patient originally had no white blood cells (i.e. the cancer had caused all white blood cells to die off);

At x = 0, y= 0.0175

Therefore, the original amount of cancer cells was 0.0175 mg/mL