You mix $50 \mathrm{~mL}$ of a $5 imes 10^{5}$ cells $/ \mathrm{mL}$ culture with $150 \mathrm{~mL}$ of a $1.5 imes 10^{6}$ cells $/ \mathrm{mL}$ culture. What is the final cell density of the mixture?

Question

You mix $50 \mathrm{~mL}$ of a $5 	imes 10^{5}$ cells $/ \mathrm{mL}$ culture with $150 \mathrm{~mL}$ of a $1.5 	imes 10^{6}$ cells $/ \mathrm{mL}$ culture. What is the final cell density of the mixture?

Accepted Answer

***A*** ∻Key Concept∻ ⚹Calculating combined cell density⚹ ∻Explanation∻ ⚹To find the final cell density of a mixture, multiply the volume of each culture by its cell density, sum these products, and then divide by the total volume of the mixture.⚹ To calculate the final cell density of the mixture, we use the formula: $$ \text{Final cell density} = \frac{(V_1 \times C_1) + (V_2 \times C_2)}{V_1 + V_2} $$ Where: - $ V_1 $ and $ V_2 $ are the volumes of the two cell cultures. - $ C_1 $ and $ C_2 $ are the cell densities of the two cell cultures. Plugging in the values from the question: $$ \text{Final cell density} = \frac{(50 \times 5 \times 10^5) + (150 \times 1.5 \times 10^6)}{50 + 150} $$ $$ \text{Final cell density} = \frac{(25 \times 10^6) + (225 \times 10^6)}{200} $$ $$ \text{Final cell density} = \frac{250 \times 10^6}{200} $$ $$ \text{Final cell density} = 1.25 \times 10^6 \text{ cells/mL} $$ So the final cell density of the mixture is $ 1.25 \times 10^6 $ cells/mL.◊What formula can be used to calculate the final cell density after mixing two cell cultures?⍭ Generate me a similar question◊

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