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QuestionNancy is mixing a 1,100-gram herb salt costing \$4.10/gram. How many grams of sea salt and dried herbs are needed?

Studdy Solution

STEP 1

Assumptions1. The total weight of the herb salt is1,100 grams. . The cost of the herb salt is 4.10pergram.<br/>3.ThecostoftheFrenchseasaltis4.10 per gram.<br />3. The cost of the French sea salt is 5.00 per gram.
4. The cost of the dried herbs is $.00 per gram.
5. The herb salt is made by combining only these two ingredients French sea salt and dried herbs.

STEP 2

Let's denote the weight of the French sea salt as xx grams and the weight of the dried herbs as yy grams. We know that the total weight of the herb salt is1,100 grams, so we can write the following equationx+y=1,100x + y =1,100

STEP 3

We also know that the cost of the herb salt is a combination of the cost of the French sea salt and the dried herbs. So, we can write another equation5x+2y=.10×1,1005x +2y =.10 \times1,100

STEP 4

We can simplify the second equationx+2y=4,510x +2y =4,510

STEP 5

Now we have a system of two equations\begin{align*} x + y &=1,100 \\ 5x +2y &=4,510\end{align*}

STEP 6

To solve this system, we can multiply the first equation by22x+2y=2,2002x +2y =2,200

STEP 7

Now we subtract the new first equation from the second equation5x+2y−(2x+2y)=4,510−2,2005x +2y - (2x +2y) =4,510 -2,200

STEP 8

This simplifies to3x=2,3103x =2,310

STEP 9

Now we can solve for xx by dividing both sides of the equation by3x=2,3103x = \frac{2,310}{3}

STEP 10

Calculate the value of xxx=2,3103≈770x = \frac{2,310}{3} \approx770So, Nancy needs approximately770 grams of French sea salt.

STEP 11

Now we can substitute xx into the first equation to find yy770+y=,100770 + y =,100

STEP 12

olve for yyy=,100−770y =,100 -770

STEP 13

Calculate the value of yyy=,100−770=330y =,100 -770 =330So, Nancy needs330 grams of dried herbs.
ancy needs approximately770 grams of French sea salt and330 grams of dried herbs for this batch.

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