craig runs a clothing store. he has decided to apply a markdown of 30% to one item in order to draw…

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?\na. wristwatch\nb. leather jacket\nc. boots\nd. blazer

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?\na. wristwatch\nb. leather jacket\nc. boots\nd. blazer

Answer

Answer:

d. blazer

Explanation:

Step1: Calculate initial total cost

$112.75 + 76.85+134.50 + 89.65=413.75$

Step2: Set up equation for final total cost

Let the marked - down item cost be $x$ initially. The final total cost is $413.75+29.46 = 443.21$.

Step3: Consider markup and markdown

If the marked - down item has an initial cost $x$ and a 30% markdown, its new cost is $0.7x$. The other three items have a 25% markup, so their new cost is $1.25$ times their initial cost. Let's test each option:

Test for wristwatch

Initial cost of wristwatch $x = 89.65$. New total cost: $1.25\times(112.75 + 76.85+134.50)+0.7\times89.65$ $=1.25\times324.1+0.7\times89.65$ $=405.125 + 62.755=467.88\neq443.21$

Test for leather jacket

Initial cost of leather jacket $x = 112.75$. New total cost: $1.25\times(76.85 + 134.50+89.65)+0.7\times112.75$ $=1.25\times301+0.7\times112.75$ $=376.25+78.925 = 455.175\neq443.21$

Test for boots

Initial cost of boots $x = 134.50$. New total cost: $1.25\times(112.75 + 76.85+89.65)+0.7\times134.50$ $=1.25\times279.25+0.7\times134.50$ $=349.0625+94.15 = 443.2125\approx443.21$

Test for blazer

Initial cost of blazer $x = 76.85$. New total cost: $1.25\times(112.75 + 134.50+89.65)+0.7\times76.85$ $=1.25\times336.9+0.7\times76.85$ $=421.125+53.795 = 474.92\neq443.21$ So the item marked down is the blazer.