To determine when the strains will have the same number of​ cells, first write and solve a system of two linear equations.

Question

A group of scientists studied the effect of a chemical on various strains

of bacteria. Strain A started with

9000

cells and decreased at a constant rate of

3000

cells per hour after the chemical was applied. Strain B started with

4000

cells

and decreased at a constant rate of

2000

cells per hour after the chemical was

applied. When will the strains have the same number of​ cells? Explain.

Answer 1

Let A and B be the number of each bacteria and t be the time in hours.

Strain A:

A=9000-3000t

Strain B:

B=4000-2000t

Setting the numbers equal

9000-3000t = 4000-2000t

Solving for t

5000 = 1000t

t = 5000/1000 = 5 hours

Which doesn't make sense since A and B must be ≥ 0, not -6000.

Strain A will be totally depleted after 3 hours and Strain B will be totally depleted after 2 hours.

So, after 3 hours, both strains will be zero.

Answer 2

Let t be the number of hours until the strains have the same number of cells

9000 - 3000t = 4000 - 2000t

Solve for t.