Question

A certain TV can be purchased from the manufacturer for $160. A certain online retailer has a standard markup of 30%, and a certain superstore has a standard markup of 40%.

(a) What is the price of the TV when purchased online? What is the price of the TV when purchased at the superstore?
(b) What is the difference between the prices in Part (a)? How does this relate to the difference in the markup?

Answer 1

(a)

Answer:

The price of the TV purchased online is $208

The price of the TV purchased at the superstore is $224

Explanation

To solve this, we are going to use the markup formula solved for price:

$Price=markup*cost+cost$

where

$markup$ is expressed in decimal form

- For the online retailer:

We know that the the TV can be purchased from the manufacturer for $160, so $cost=160$. We also know that its markup is 30%; to express the markup as a decimal, we just need to divide it by 100%, so $markup=\frac{30}{100} =0.3$. Now we can replace the values in our formula to find the price of the TV at the online retailer:

$Price=markup*cost+cost$

$Price=0.3*160+160$

$Price=48+160$

$Price=208$

The price of the TV purchased online is $208

- For the superstore:

The cost is the same, so $cost=160$. The markup this time is 40%, so $markup=\frac{40}{100}=0.4$. Let's replace the values to find the price:

$Price=0.4*160+160$

$Price=64+160$

$Price=224$

The price of the TV purchased at the superstore is $224

(b)

Answer

The difference between the prices is $16

The difference relates to the markup in two ways:

- When the markup increases 10% (from 30% to 40%), the price of the TV increases by $16.

- When the markup increases 10% (from 30% to 40%), the price of the TV increases 7.7%.

Explanation

To find the difference of our prices, we just need to subtract the price of the TV purchased at the superstore from the price of the TV purchased online:

$224 - $208 = $16

Now, to find how much the cost increased when the markup increases from 30% to 40%, we are going to divide the result of the difference of the two prices by the price of the TV at the online retailer, and then multiply by 100%:

$\frac{16}{208} *100=7.69$

Which rounds to 7.7%

We can conclude that when the markup increases 10% (from 30% to 40%), the price of the TV increases 7.7%.

We can also conclude that when the markup increases 10% (from 30% to 40%), the price of the TV increases by $16.