ashley runs a hardware store. she has decided to apply a markdown of 15% to one item in order to draw…

ashley runs a hardware store. she has decided to apply a markdown of 15% to one item in order to draw customers into the store, and she will apply a markup of 10% to three different items, which she hopes the customers will purchase after purchasing the marked - down item. she has chosen four candidates for this process: a power drill with an initial price of $51.49, a ceiling fan with an initial price of $64.79, a miniature circular saw with an initial price of $45.99, and a screwdriver set with an initial price of $37.39. after applying the changes, the total cost of purchasing one of each item is $3.77 more than it was before applying the changes. which item was marked down?\na. power drill\nb. ceiling fan\nc. circular saw\nd. screwdriver set

ashley runs a hardware store. she has decided to apply a markdown of 15% to one item in order to draw customers into the store, and she will apply a markup of 10% to three different items, which she hopes the customers will purchase after purchasing the marked - down item. she has chosen four candidates for this process: a power drill with an initial price of $51.49, a ceiling fan with an initial price of $64.79, a miniature circular saw with an initial price of $45.99, and a screwdriver set with an initial price of $37.39. after applying the changes, the total cost of purchasing one of each item is $3.77 more than it was before applying the changes. which item was marked down?\na. power drill\nb. ceiling fan\nc. circular saw\nd. screwdriver set

Answer

Explanation:

Step1: Calculate the total initial cost

Let the initial prices of power - drill, ceiling fan, circular saw, and screwdriver set be $p_1 = 51.49$, $p_2=64.79$, $p_3 = 45.99$, $p_4 = 37.39$ respectively. The total initial cost $C_{initial}=p_1 + p_2 + p_3 + p_4=51.49+64.79 + 45.99+37.39=200.66$.

Step2: Calculate the total final cost

The total final cost $C_{final}=C_{initial}+3.77=200.66 + 3.77=204.43$.

Step3: Let the marked - down item's initial price be $x$ and the other three items' initial prices be $y_1,y_2,y_3$.

The final price of the marked - down item is $0.85x$ (since it has a 15% markdown), and the final prices of the other three items are $1.1y_1,1.1y_2,1.1y_3$ (since they have a 10% markup). So, $0.85x+1.1y_1 + 1.1y_2+1.1y_3=204.43$ and $x + y_1 + y_2 + y_3=200.66$, which means $y_1 + y_2 + y_3=200.66 - x$. Substitute into the first equation: $0.85x+1.1(200.66 - x)=204.43$.

Step4: Expand and solve the equation

Expand $0.85x+1.1(200.66 - x)=204.43$: $0.85x+220.726-1.1x = 204.43$. Combine like - terms: $0.85x-1.1x=204.43 - 220.726$. $- 0.25x=-16.296$. Solve for $x$: $x=\frac{-16.296}{-0.25}=64.784\approx64.79$.

Answer:

b. ceiling fan