nancy has a home - based business selling herb and spice mixes. she is currently mixing up a 1,100 - gram…

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

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

Answer

Explanation:

Step1: Set up equations

Let $x$ be the grams of French sea - salt and $y$ be the grams of dried herbs. We have two equations: $x + y=1100$ (total weight equation) and $5x + 2y=4.1\times1100$ (cost - based equation).

Step2: Express $y$ from the first equation

From $x + y=1100$, we get $y = 1100 - x$.

Step3: Substitute $y$ into the second equation

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

Step4: Solve for $x$

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

Step5: Solve for $y$

Substitute $x = 770$ into $y = 1100 - x$. So $y=1100 - 770 = 330$.

Answer:

770 grams of French sea salt 330 grams of dried herbs