Craig runs a clothing store. he has decided to apply a markdown of 30% to one item in order to draw customers into the store, and he will apply a markup of 25% to three different items, which he hopes the customers will purchase after purchasing the marked-down item. he has chosen four candidates for this process: a leather jacket with an initial cost of $112.75, a blazer with an initial cost of $76.85, a pair of boots with an initial cost of $134.50, and a wristwatch with an initial price of $89.65. after applying the changes, the total cost of purchasing one of each item is $29.46 more than it was before applying the changes. which item was marked down?

The pair of boats was marked down.

Step-by-step explanation:  Given that in his clothing store, Craig decided to apply a markdown of 30% to one item in order to draw customers into the store, and he will apply a markup of 25% to three different items.

The four items chosen were

a leather jacket with an initial cost of $112.75,

a blazer with an initial cost of $76.85,

a pair of boot with an initial cost of $134.50,

and a wrst watch with an initial price of $89.65.

After applying the changes,  the total cost of purchasing one of each item is $29.46 more than it was before applying the changes.

We are to find the item that is marked below.

We will be choosing the items one by one and will find the profit by applying mark up and mark down percentage to match the total profit with $29.46.

If the mark down item was the leather jacket, then the total profit will be given by

P = 25% × (76.85+134.50+89.65)-30% × 112.75

  = 0.25 × 301 - 0.30 × 112.75

  = 75.25 - 33.825

  = 41.425 ≠ 29.46.

So, the leather jacket was not marked down.

If the mark down item was the blazer, then the total profit will be given by

P = 25% × (112.75+134.50+89.65) - 30% × 76.85

   = 0.25 × 336.9 - 0.30 × 76.85

   = 84.225 - 23.055

   = 61.17 ≠ 29.46.

So, the blazer was not marked down.

If the mark down item was the pair of boot, then the total profit will be given by

P = 25% × (112.75+76.85+89.65) - 30% × 134.50

   = 0.25 × 279.25 - 0.30 × 134.50

   = 69.8125 - 40.35

   = 29.4625 = 29.46.

So, the pair of boot was marked down.

If the mark down item was the wrst watch, then the total profit will be given by

P = 25% × (112.75+76.85+134.50) - 30%× 89.65

   = 0.25 × 324.1 - 0.30 × 89.65

   = 81.025 - 26.895

   = 54.13 ≠ 29.46.

So, the wrst watch was not marked down.

Thus, the marked down item was pair of boot.

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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