Mark up value is either a fixed amount or a percentage of the total cost or selling price.
In this problem, mark up value is the percentage of the total cost.
To determine the retail price, total cost and mark up must be added.
Selling Price = Total Cost + Mark up value based on Total Cost
However, we are looking for the Total cost. Thus, our formula should be
Total Cost = Selling Price - Mark up value based on Total Cost.
Let X = total cost.
Selling Price = $8,000
Mark up vale = 6% of total cost.
X = $8,000 - 6%X
X = $8,000 - 0.06X
To get X, transfer -0.06X to the other side and change its sign from negative to positive.
X + 0.06X = $8000
1.06X = $8000
To get X, divide both sides by 1.06
1.06X / 1.06 = $8000 / 1.06
X = $7,547.17 total cost.
The problem is looking for the mark up value and since it states that the mark up value is 6% of the total cost, then:
Total Cost x 6% = Mark up value
$7,547.17 x 0.06 = $452.83 mark up value
To check:
X + 0.06X = $8000
$7547.17 + $452.83 = $8000
$8000 = $8000 equal.