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A seasoning blend is 4% onion powder, by mass.
How much pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder?

◻ g

A seasoning blend is $4\%$ onion powder, by mass. $\newline$ How much pure onion powder should they include in a $72\,\text{g}$ bottle to make the final blend have $20\%$ onion powder? $\newline$ $\square\,\text{g}$

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Weighted averages: word problems

Full solution

Q. A seasoning blend is

4\%

onion powder, by mass.

\newline

How much pure onion powder should they include in a

72\,\text{g}

bottle to make the final blend have

20\%

onion powder?

\newline

\square\,\text{g}

Identify Concentration: We need to find the amount of pure onion powder to add to reach $20\%$ concentration in a $72g$ bottle.
Define Variable: Let $x$ be the amount of pure onion powder to add.
Calculate Remaining Amount: The rest of the bottle will be filled with the original $4\%$ onion powder blend, which will be $72g - x$ .
Total Mass of Onion Powder: The total mass of onion powder in the new blend will be $x$ (from the pure onion powder) plus $0.04(72 - x)$ (from the $4\%$ blend).
Set Up Equation: We want the total mass of onion powder to be $20\%$ of the total mass of the blend, which is $72g$ . So, we set up the equation: $x + 0.04(72 - x) = 0.20 \times 72$ .
Solve Equation: Solving the equation: $x + 2.88 - 0.04x = 14.4$ .
Combine Like Terms: Combine like terms: $x - 0.04x = 14.4 - 2.88$ .
Divide to Solve: $0.96x = 11.52$ .
Calculate Final Value: Divide both sides by $0.96$ to solve for $x$ : $x = \frac{11.52}{0.96}$ .
Calculate Final Value: Divide both sides by $0.96$ to solve for $x$ : $x = \frac{11.52}{0.96}$ .Calculate the value of $x$ : $x = 12$ .

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