QuestionJune 2, 2025

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 12000 cells and decreased at a constant rate of 4000 cells per hour after the chemical was applied. Strain B started with 6000 cells and decreased at a constant rate of 3000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain. To determine when the strains will have the same number of cells first write and solve a system of two linear equations The solution to the system of linear equations is square (Type an ordered pair,but do not use commas in any individual coordinates.)

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 12000 cells and decreased at a constant rate of 4000 cells per hour after the chemical was applied. Strain B started with 6000 cells and decreased at a constant rate of 3000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain. To determine when the strains will have the same number of cells first write and solve a system of two linear equations The solution to the system of linear equations is square (Type an ordered pair,but do not use commas in any individual coordinates.)
A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 12000 cells and decreased at a constant rate of 4000 cells per hour after the chemical was applied. Strain B started with 6000 cells and decreased at a constant rate of 3000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain. To determine when the strains will have the same number of cells first write and solve a system of two linear equations The solution to the system of linear equations is square (Type an ordered pair,but do not use commas in any individual coordinates.)

Solution
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Answer

(6 -12000) Explanation 1. Write equations for each strain Strain A: y = 12000 - 4000x; Strain B: y = 6000 - 3000x 2. Set equations equal to find intersection 12000 - 4000x = 6000 - 3000x 3. Solve for x Rearrange: 12000 - 6000 = 4000x - 3000x Simplify: 6000 = 1000x Divide: x = 6 4. Substitute x back to find y Use Strain A equation: y = 12000 - 4000(6) Calculate: y = 12000 - 24000 = -12000

Explanation

1. Write equations for each strain<br /> Strain A: $y = 12000 - 4000x$; Strain B: $y = 6000 - 3000x$<br /><br />2. Set equations equal to find intersection<br /> $12000 - 4000x = 6000 - 3000x$<br /><br />3. Solve for x<br /> Rearrange: $12000 - 6000 = 4000x - 3000x$<br /> Simplify: $6000 = 1000x$<br /> Divide: $x = 6$<br /><br />4. Substitute x back to find y<br /> Use Strain A equation: $y = 12000 - 4000(6)$<br /> Calculate: $y = 12000 - 24000 = -12000$
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