1) markup = $105 , selling price = $150 , %mark up based on cost = 233.33% , mark down = $30 , sale price = $120
2) mark up = $75.08 , selling price = $110.83 , %mark up based on selling price = 67.74% , mark down = $27.71 , sale price = $83.12
3) Cost = $19.87 , markup = $59.62 , %markup based on selling price = 75% , mark down = $19.87 , sale price = $59.62
4) Cost = $9.72 , mark up = $3.24 , %mark up based on cost = 33.33% , %mark down = 10.03% , sale price = $11.66
5) Cost = $17.9 , selling price = $53.7 , %markup based on selling price = 66.67% , Mark down = 10.74 , %markdown = 20% ,
Step-by-step explanation:
1) ∵ cost/complement of %mark up based on selling price = selling price
∴ Selling price = 45/(1 - 0.7) = $150
∵ Mark up = selling price - cost price
∴ Mark up = 150 - 45 = $105
∵ %mark up based on cost price = mark up /cost
∴ %mark up based on cost price = 105/45 = 233.33%
∵ Mark down = selling price × %mark down
∴ Mark down = 150 × 0.2 = $30
∵ Sale price = selling price - mark down
∴ Sale price = 150 - 30 = $120
2) ∵ Mark up = Cost × %mark up based on the cost
∴ Mark up = 35.75 × 2.1 = $75.08
∵ Selling price = cost + markup
∴ Selling price = 35.75 + 75.08 = $110.83
∵ %markup based on selling price = mark up/selling price
∴ %markup based on selling price = 75.08/110.83 = %67.74
∵ Mark down = selling price × %mark down
∴ Mark down = 110.83 × 0.25 = $27.71
∵ Sale price = selling price - mark down
∴ sale price = 110.83 - 27.71 = $83.12
3) ∵ Mark down = selling price × %mark down
∴ Mark down = 79.49 × 0.25 = $19.87
∵ Sale price = selling price - mark down
∴ Sale price = 79.49 - 19.87 = $59.62
∵ Mark up/cost = %mark up based on cost
∴ Mark up/cost = 3
∴ Mark up = 3 cost ⇒ (1)
∵ Mark up + cost = selling price
∴ Mark up + cost = 79.49 ⇒ (2)
∵ Sub (1) in (2)
∴ 3cost + cost = 79.49 ⇒ 4cost = 79.49 ⇒ cost = 79.49/4
∴ Cost = $19.87
∴ Mark up = 3 × 19.87 = $59.62
∵ %mark up = mark up/selling price
∴ % mark up = 59.62/79.49 = 75%
4) ∵ Mark up = selling price × % mark up based on selling price
∴ Mark up = 12.96 × 0.25 = $3.24
∵ Cost = complement of %mark up based on selling price × selling price
∵ Cost = (1 - 0.25) × 12.96 = $9.72
∵ %mark up based on cost = mark up/cost
∴ %mark up based on cost = 3.24/9.72 = 33.33%
∵ %Mark down = mark down/ selling price
∴ %Mark down = 1.30/12.96 = 10.03%
∵ Sale price = selling price - mark down
∴ Sale price = 12.96 - 1.30 = $11.66
5) ∵ Cost = mark up/%mark up based on cost
∴ Cost = 35.8/2 = $17.9
∵ Selling price = cost + mark up
∴ Selling price = 17.9 + 35.8 = $53.7
∵ Complementary of %mark up on selling price = cost/selling price
∴ Complementary of %mark up on selling price = (17.9/53.7) × 100 = 33.33%
∴ %mark up on selling price = 100 - 33.33 = 66.67%
∵ Mark down = selling price - sale price
∴ Mark down = 53.7 - 42.96 = $10.74
∵ % mark down = mark down/selling price
∴ % Mark down = 10.74/53.7 = 20%
