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\nplease select the best answer from the choices provided

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\nplease select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate the total initial cost

Let the initial cost of the leather - jacket be $L = 112.75$, the blazer be $B=76.85$, the boots be $O = 134.50$, and the wrist - watch be $W = 89.65$. The total initial cost $T_{initial}=L + B+O + W=112.75+76.85 + 134.50+89.65=413.75$.

Step2: Calculate the total final cost

The total final cost $T_{final}=T_{initial}+29.46=413.75 + 29.46=443.21$.

Step3: Let the marked - down item be $x$.

The cost of the three marked - up items is $(1 + 0.25)$ times their original cost, and the cost of the marked - down item is $(1 - 0.30)$ times its original cost. Let's assume the marked - down item is the leather - jacket. Then the equation for the final cost is $0.7L+1.25B + 1.25O+1.25W$. Substitute the values: $0.7\times112.75+1.25\times76.85+1.25\times134.50+1.25\times89.65=78.925+96.0625+168.125+112.0625=455.175\neq443.21$. Let's assume the marked - down item is the blazer. Then the equation for the final cost is $1.25L+0.7B + 1.25O+1.25W$. Substitute the values: $1.25\times112.75+0.7\times76.85+1.25\times134.50+1.25\times89.65=140.9375 + 53.795+168.125+112.0625=474.92\neq443.21$. Let's assume the marked - down item is the boots. Then the equation for the final cost is $1.25L+1.25B+0.7O + 1.25W$. Substitute the values: $1.25\times112.75+1.25\times76.85+0.7\times134.50+1.25\times89.65=140.9375+96.0625 + 94.15+112.0625=443.21$. Let's assume the marked - down item is the wrist - watch. Then the equation for the final cost is $1.25L+1.25B+1.25O+0.7W$. Substitute the values: $1.25\times112.75+1.25\times76.85+1.25\times134.50+0.7\times89.65=140.9375+96.0625+168.125+62.755=467.88\neq443.21$.

Answer:

C. boots