The markup over dealer's cost of a new car ranges from 18% to 24%. If the sticker price is $14000 over what range will the dealer's cost vary?
The cost with a 18% markup
= 14000/1.18 = $11 864.41
cost with a 24% markup
= 14000/1.24 = $11 290.32
To determine the range within which the dealer's cost will vary, we need to calculate the minimum and maximum dealer's cost based on the given markup percentages.
First, let's find the maximum dealer's cost:
The markup of 24% over the dealer's cost would be a total markup of $14,000 according to the given information.
Let's assume the dealer's cost is represented by 'C'. The equation would be:
C + 24% of C = C + 0.24C = C(1 + 0.24) = C(1.24)
According to the given information, the total markup is $14,000, so:
C(1.24) = C + $14,000
Subtracting C from both sides:
0.24C = $14,000
Dividing both sides by 0.24:
C = $14,000 / 0.24
C ≈ $58,333.33 (dealer's cost)
Now, let's find the minimum dealer's cost:
The markup of 18% over the dealer's cost would be a total markup of $14,000 according to the given information.
The equation would be:
C + 18% of C = C + 0.18C = C(1 + 0.18) = C(1.18)
According to the given information, the total markup is $14,000, so:
C(1.18) = C + $14,000
Subtracting C from both sides:
0.18C = $14,000
Dividing both sides by 0.18:
C = $14,000 / 0.18
C ≈ $77,777.78 (dealer's cost)
Therefore, the dealer's cost of the new car will vary between approximately $58,333.33 and $77,777.78.
To find the range of the dealer's cost, we need to calculate the range based on the given markup percentages.
Step 1: Calculate the minimum markup:
Minimum Markup = Dealer's Cost x Markup Percentage (18%)
Step 2: Calculate the maximum markup:
Maximum Markup = Dealer's Cost x Markup Percentage (24%)
Step 3: Calculate the sticker price:
Sticker Price = Dealer's Cost + Maximum Markup
Given that the sticker price is $14,000 over the dealer's cost, we can use this information to set up an equation:
Sticker Price = Dealer's Cost + Maximum Markup
$14,000 = Dealer's Cost + Dealer's Cost x Markup Percentage (24%)
Rearranging the equation, we have:
$14,000 = Dealer's Cost (1 + Markup Percentage)
Now, we can substitute the minimum and maximum markup percentages:
$14,000 = Dealer's Cost (1 + 18%)
$14,000 = Dealer's Cost (1 + 0.18)
Simplifying the equation:
$14,000 = Dealer's Cost (1.18)
Dividing both sides by 1.18:
Dealer's Cost = $14,000 / 1.18
Calculating the dealer's cost:
Dealer's Cost = $11,864.41 (rounded)
Now, we can find the range of the dealer's cost using the minimum and maximum markup percentages:
Minimum Dealer's Cost = Dealer's Cost - Dealer's Cost x Markup Percentage (18%)
Minimum Dealer's Cost = $11,864.41 - $11,864.41 x 18%
Maximum Dealer's Cost = Dealer's Cost - Dealer's Cost x Markup Percentage (24%)
Maximum Dealer's Cost = $11,864.41 - $11,864.41 x 24%
Calculating the minimum and maximum dealer's cost:
Minimum Dealer's Cost ≈ $9,708.21
Maximum Dealer's Cost ≈ $8,999.60
Therefore, the dealer's cost of the new car will vary from approximately $8,999.60 to $9,708.21.