Question

nancy has a home - based business selling herb and spice mixes. she is currently mixing up a 1,100 - gram batch of her popular herb salt, which costs $4.10 per gram. it is made by combining fine french sea salt, which costs $5.00 per gram, with organic dried herbs, which cost $2.00 per gram. how many grams of each ingredient will nancy need for this batch? write your answers as whole numbers or as decimals rounded to the nearest tenth. grams of french sea salt grams of dried herbs

Explanation:

Step1: Let the amount of French sea salt be $x$ grams and the amount of dried herbs be $y$ grams.

We know two - equations based on the total amount and the cost. The total - amount equation is $x + y=1100$ (since the total batch is 1100 grams), so $y = 1100 - x$. The cost - based equation is $5x+2y=4.1\times1100$.

Step2: Substitute $y = 1100 - x$ into the cost - based equation.

$5x+2(1100 - x)=4.1\times1100$. Expand the left - hand side: $5x + 2200-2x=4510$. Combine like terms: $3x+2200 = 4510$.

Step3: Solve for $x$.

Subtract 2200 from both sides: $3x=4510 - 2200=2310$. Then divide both sides by 3: $x=\frac{2310}{3}=770$ grams.

Step4: Solve for $y$.

Since $y = 1100 - x$, substitute $x = 770$ into this equation. So $y=1100 - 770 = 330$ grams.

Answer:

770 grams of French sea salt
330 grams of dried herbs