Final answer:
To achieve a 20% concentration of onion powder in a 72g bottle, a student needs to add 14.40 g of pure onion powder to the current blend containing 4% onion powder.
Step-by-step explanation:
The question is asking how much pure onion powder should be included in a 72 g bottle to ensure the final blend has 20% onion powder. To solve this, we will use the mass percentage concept, which is a common way to express concentration in consumer products such as liquid bleach. The concentration is given by the mass of the solute (in this case, onion powder) divided by the total mass of the solution (the entire seasoning blend), multiplied by 100 to get the percentage.
First, we calculate the current amount of onion powder in the bottle:
- Original percentage of onion powder = 4%
- The total mass of the blend = 72 g
- Current mass of onion powder = 0.04 × 72 g = 2.88 g
Now, we use the following equation to find out how much pure onion powder we need to add to achieve the 20% concentration:
(Mass of pure onion powder to add + Current mass of onion powder) / Total mass of new blend = Desired percentage
Let's denote the mass of pure onion powder to add as x.
(x + 2.88 g) / (72 g + x) = 0.20
Solving for x:
x + 2.88 g = 0.20 × (72 g + x)
x + 2.88 g = 14.4 g + 0.20x
x - 0.20x = 14.4 g - 2.88 g
0.80x = 11.52 g
x = 11.52 g / 0.80
x = 14.40 g. So, the student should add 14.40 g of pure onion powder to the blend.