Question

Karen is making scented oil, mixing rose oil that costs $10.00 per ounce with sweet almond oil that costs $1.25 per ounce. Overall, the blend ends up costing $8.25 per ounce. If Karen has 4 ounces of rose oil, how many ounces of almond oil will she need to make the blend?

Answer 1

To create a blend that costs $8.25 per ounce using 4 ounces of rose oil ($10/oz) and sweet almond oil ($1.25/oz), Karen needs 1 ounce of sweet almond oil.

Step-by-step explanation:

The question asks us to calculate the amount of sweet almond oil required to create a scented oil blend with a specific cost per ounce. Karen has 4 ounces of rose oil at $10.00 per ounce and wishes to blend it with sweet almond oil costing $1.25 per ounce to achieve a final blend cost of $8.25 per ounce.

Step-by-step Explanation

1. Firstly, calculate the total cost of rose oil by multiplying the number of ounces Karen has (4 ounces) by the cost per ounce ($10.00). That's a total of $40.00 for the rose oil.
2. Next, let the number of ounces of sweet almond oil needed be x. Multiply x by the cost per ounce of almond oil ($1.25) to get the total cost of the almond oil.
3. The total cost of the blend will be the cost of the rose oil plus the cost of the almond oil, which equals the number of total ounces times the target cost per ounce ($8.25).
4. Set up the equation $40 + 1.25x = 8.25(4 + x)
5. Solve the equation for x. First, distribute the $8.25 across the right side of the equation yielding $33 + 8.25x. Now, set up a new equation 1.25x - 8.25x = $33 - $40.
6. Combining like terms, this leads to -7x = -$7. Divide both sides by -7 to get x = 1.
7. Karen needs 1 ounce of sweet almond oil to achieve the desired blend.