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? a. power drill b. ceiling fan c. circular saw d. 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? a. power drill b. ceiling fan c. circular saw d. screwdriver set

Answer

Explanation:

Step1: Calculate the total initial price

Let the initial prices of the power - drill, ceiling fan, circular saw, and screwdriver set be $p = 51.49$, $c=64.79$, $s = 45.99$, and $d = 37.39$ respectively. The total initial price $T_{initial}=p + c + s + d=51.49+64.79+45.99+37.39 = 200.66$.

Step2: Calculate the total final price

The total final price $T_{final}=T_{initial}+3.77=200.66 + 3.77=204.43$.

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 equation is $(1 - 0.15)x+(1 + 0.1)(y_1 + y_2 + y_3)=204.43$, and $x + y_1 + y_2 + y_3=200.66$, so $y_1 + y_2 + y_3=200.66 - x$.

Substitute $y_1 + y_2 + y_3$ into the first equation: $0.85x+1.1(200.66 - x)=204.43$.

Step4: Expand and solve the equation

Expand the left - hand side: $0.85x+220.726-1.1x = 204.43$. Combine like terms: $220.726-(1.1x - 0.85x)=204.43$, $220.726 - 0.25x=204.43$. Subtract 220.726 from both sides: $-0.25x=204.43 - 220.726=-16.296$. Divide both sides by $- 0.25$: $x=\frac{-16.296}{-0.25}=65.184\approx64.79$.

Answer:

b. ceiling fan