he wholesale cost of a delivery van is $31,300. The original markup was 26% based on selling price. Find the final sale price after the following series of price changes: a markup of 46%, a markup of 15%, a markdown of 40%, and a markup of 14%. (Round each selling price to the nearest cent)
To find the final sale price after a series of price changes, we need to calculate the selling price after each price change and then apply the subsequent price change to the new selling price.
1. The original markup of 26% based on the selling price:
Selling price after the original markup = Cost + Markup
Markup = 26% of the selling price
Selling price after the original markup = $31,300 + (26% of the selling price)
2. A markup of 46%:
Selling price after the 46% markup = Selling price after the original markup + (46% of the selling price after the original markup)
3. A markup of 15%:
Selling price after the 15% markup = Selling price after the previous markup + (15% of the selling price after the previous markup)
4. A markdown of 40%:
Selling price after the 40% markdown = Selling price after the previous markup - (40% of the selling price after the previous markup)
5. A markup of 14%:
Selling price after the 14% markup = Selling price after the previous markdown + (14% of the selling price after the previous markdown)
Let's calculate the final sale price step by step:
1. Selling price after the original markup:
Selling price after the original markup = $31,300 + (26% x Selling price)
Selling price after the original markup = $31,300 + 0.26 x Selling price
2. Selling price after the 46% markup:
Selling price after the 46% markup = Selling price after the original markup + (46% x Selling price after the original markup)
Selling price after the 46% markup = [$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]
3. Selling price after the 15% markup:
Selling price after the 15% markup = Selling price after the previous markup + (15% x Selling price after the previous markup)
Selling price after the 15% markup = [[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]
4. Selling price after the 40% markdown:
Selling price after the 40% markdown = Selling price after the previous markup - (40% x Selling price after the previous markup)
Selling price after the 40% markdown = [[[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]] - 0.40 x [[[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]]]
5. Selling price after the 14% markup:
Selling price after the 14% markup = Selling price after the previous markdown + (14% x Selling price after the previous markdown)
Selling price after the 14% markup = [[[[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]] - 0.40 x [[[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]]]] + 0.14 x [[[[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]] - 0.40 x [[[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]] + 0.15 x [[[$31,300 + 0.26 x Selling price] + 0.46 x [$31,300 + 0.26 x Selling price]]]]]]]
Unfortunately, we don't have the initial value for the selling price to calculate the final sale price. Please provide the initial selling price, or any additional information you have so that we can assist you further.
To find the final sale price after a series of price changes, we'll need to apply each price change one by one. Let's start with the original markup of 26% based on the selling price.
1. Markup of 26%: To find the selling price after this markup, we need to add 26% of the selling price to the wholesale cost.
Markup = 26% of selling price = 0.26 * Selling Price
Selling Price = Wholesale cost + Markup = $31,300 + 0.26 * Selling Price
Now let's apply the following series of price changes step by step:
2. Markup of 46%: We need to add 46% of the current selling price.
Selling Price = Previous Selling Price + 0.46 * Previous Selling Price
3. Markup of 15%: We need to add 15% of the current selling price.
Selling Price = Previous Selling Price + 0.15 * Previous Selling Price
4. Markdown of 40%: We need to subtract 40% of the current selling price.
Selling Price = Previous Selling Price - 0.40 * Previous Selling Price
5. Markup of 14%: We need to add 14% of the current selling price.
Selling Price = Previous Selling Price + 0.14 * Previous Selling Price
We'll repeat these steps until we reach the final sale price.
Let's calculate step by step:
1. Markup of 26%:
Selling Price = $31,300 + 0.26 * Selling Price
Selling Price = $31,300 / (1 - 0.26)
Selling Price = $31,300 / 0.74
Selling Price = $42,297.30 (rounded to the nearest cent)
2. Markup of 46%:
Selling Price = $42,297.30 + 0.46 * $42,297.30
Selling Price = $42,297.30 * (1 + 0.46)
Selling Price = $42,297.30 * 1.46
Selling Price = $61,626.53 (rounded to the nearest cent)
3. Markup of 15%:
Selling Price = $61,626.53 + 0.15 * $61,626.53
Selling Price = $61,626.53 * (1 + 0.15)
Selling Price = $61,626.53 * 1.15
Selling Price = $70,870.51 (rounded to the nearest cent)
4. Markdown of 40%:
Selling Price = $70,870.51 - 0.40 * $70,870.51
Selling Price = $70,870.51 * (1 - 0.40)
Selling Price = $70,870.51 * 0.60
Selling Price = $42,522.31 (rounded to the nearest cent)
5. Markup of 14%:
Selling Price = $42,522.31 + 0.14 * $42,522.31
Selling Price = $42,522.31 * (1 + 0.14)
Selling Price = $42,522.31 * 1.14
Selling Price = $48,428.93 (rounded to the nearest cent)
Therefore, the final sale price after all the price changes is approximately $48,428.93.
CHECK:
P1 + 0.26P1 = $31,300.
1.26P1 = 31,300,
P1 = 24,841.27.
P2 = 1.46P1 = 1.46 * 24,841.27 = 36,268.25.
P3 = 1.15P2 = 1.15 * 36,268.25 = 41,708.49.
P4 = (1-0.4)P3 = 0.6*41,708.49 = 25,025.10.
P5 = 1.14P4 = 1.14 * 25,025.10 = 28,528.61.
1.26n=31300
n=24841.27
1.46 x 1.15 x 0.6 x 1.14 x 24841.27=28528.61 as the final sale price.
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