a boutique owner is mixing an 18 - ounce batch of her custom salt scrub, which costs $3.40 per ounce to…

a boutique owner is mixing an 18 - ounce batch of her custom salt scrub, which costs $3.40 per ounce to make. it is made up of a tropical oil blend with a cost of $7.95 per ounce and sea salt with a cost of $1.45 per ounce. how many ounces of each should be used to make this batch? write your answers as whole numbers or as decimals rounded to the nearest tenth. ounces of tropical oil blend ounces of sea salt

a boutique owner is mixing an 18 - ounce batch of her custom salt scrub, which costs $3.40 per ounce to make. it is made up of a tropical oil blend with a cost of $7.95 per ounce and sea salt with a cost of $1.45 per ounce. how many ounces of each should be used to make this batch? write your answers as whole numbers or as decimals rounded to the nearest tenth. ounces of tropical oil blend ounces of sea salt

Answer

Answer:

Let $x$ be the number of ounces of tropical - oil blend and $y$ be the number of ounces of sea salt. We have two equations based on the given information:

  1. Total - amount equation: The total amount of the salt scrub is 18 ounces, so $x + y=18$, which can be rewritten as $y = 18 - x$.
  2. Cost - equation: The cost of the blend is based on the cost per ounce of each component. The cost of the 18 - ounce batch is $3.40\times18 = 61.2$. The cost of the tropical - oil blend is $7.95x$ and the cost of the sea salt is $1.45y$. So, $7.95x+1.45y=61.2$.

Substitute $y = 18 - x$ into the cost - equation:

Step1: Substitute $y$ into the cost - equation

$7.95x+1.45(18 - x)=61.2$ Expand the equation: $7.95x+26.1-1.45x = 61.2$

Step2: Combine like terms

$(7.95x-1.45x)+26.1 = 61.2$ $6.5x+26.1 = 61.2$

Step3: Isolate the variable term

Subtract 26.1 from both sides: $6.5x=61.2 - 26.1$ $6.5x=35.1$

Step4: Solve for $x$

Divide both sides by 6.5: $x=\frac{35.1}{6.5}=5.4$

Step5: Solve for $y$

Substitute $x = 5.4$ into $y = 18 - x$: $y=18 - 5.4 = 12.6$

5.4 ounces of tropical oil blend, 12.6 ounces of sea salt

Explanation:

Step1: Set up substitution

Replace $y$ in cost - eqn.

Step2: Simplify left - hand side

Combine $x$ terms.

Step3: Get $x$ term alone

Subtract 26.1 from both sides.

Step4: Solve for $x$

Divide by 6.5.

Step5: Solve for $y$

Substitute $x$ value into $y$ formula.