(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 @@MATH_TOKEN_2@@. We also know that its markup is 30%; to express the markup as a decimal, we just need to divide it by 100%, so @@MATH_TOKEN_3@@. Now we can replace the values in our formula to find the price of the TV at the online retailer:
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@@MATH_TOKEN_5@@
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@@MATH_TOKEN_7@@
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.
