Find the cost and markup price with the selling price of $73.99 and the markup rate of 85.4%
The correct answer and explanation is:
To find the cost and markup price, let’s break this down.
Formulae
- Selling Price (SP) = Cost (C) + Markup Price (MP)
- Markup Price (MP) = Cost × Markup Rate
- Selling Price (SP) = Cost × (1 + Markup Rate)
Given:
- Selling Price (SP) = $73.99
- Markup Rate = 85.4% (which we convert to decimal form: 0.854)
Step 1: Calculate the Cost
From the formula: SP=C×(1+Markup Rate)SP = C \times (1 + \text{Markup Rate})
Substitute the values: 73.99=C×(1+0.854)73.99 = C \times (1 + 0.854) 73.99=C×1.85473.99 = C \times 1.854
To find C (the cost), divide both sides by 1.854: C=73.991.854≈39.92C = \frac{73.99}{1.854} \approx 39.92
So, the cost of the item is approximately $39.92.
Step 2: Calculate the Markup Price
Now that we know the cost, we can calculate the markup price: MP=C×Markup RateMP = C \times \text{Markup Rate} MP=39.92×0.854≈34.12MP = 39.92 \times 0.854 \approx 34.12
So, the markup price is approximately $34.12.
Summary
- The cost of the item is approximately $39.92.
- The markup price is approximately $34.12.
This means the item was originally purchased at $39.92, and the markup (or profit added on top) is $34.12, resulting in the final selling price of $73.99.