SOLUTION: A shoe store uses a 40% markup on its cost. Find the selling price of a pair of running shoes that cost the store $40.

Question 637689: A shoe store uses a 40% markup on its cost. Find the selling price of a pair of running shoes that cost the store $40.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
There is a jillion questions of this type - mark-up, mark-down, sale price, interest earned, etc etc.
Actually the process is straight forward. If, as in your case, it asks for mark-up the selling price will be HIGHER, so you ADD.
So your answer will be higher than $40. How much higher?
Here it is 40% higher. Forty percent of what?
Forty percent of their COST. What's their cost?
It is given as $40. How do you calculate 40% of $40?
40% of $40 means that you multiply the two numbers.
BUT if you do that you get $1600, which is obviously too much for running shoes! What did I do wrong? The problem is that, although used all the time, the percentage (%) can't be used in mathematical calculations. It MUST be converted to a unitless ratio by divide the given percentage number by 100.
40% becomes 40/100
Now multiply (40/100) by the cost of $40
Mark-up is = (40/100)*40 = 1600/100 = 16. Sixteen what? Since 40/100 has no units the product has units of dollars ($).
The mark-up is $16. Whats the selling price?
Selling price = store's cost + mark-up
Selling price = 40 + 16
Selling price = 56
Your answer: The store's selling price for the running shoes is $56.
Let's omit the tutorial and calculate the selling price, S.
1) S = 40 + (40/100)*40
2) S = 40 + 0.40*40
3) S = 40 + 16
4) S = 56
Selling price is $56
Agree? Sort of easy, but I have the DrBeeee short cut. After you do several hundred of such problems and watching a store clerk calculate the sales price, you recognize that steps 2) and 3) can be replaced with one step.
In step two above, note that 40 (the base cost) factors out of each term, and we can rewrite 2) as
2)' S = 40*(1 + 0.40) then 3) becomes
3)' S = 40*(1.40)
4) S = 56
This short cut avoids the addition of 16 to the cost of 40
Understand what I did? No, stick to the first set of step a few more times. Yes, you are an extremely good learner.
Further comments.
Many problems ask for the sales price on an item listed say at $39, with a discount of 20%. We do the same as above with the exception of a MINUS sign.
Sales price = List price - Discount
S = 39 - (20/100)*39
S = 39 - 0.2*39
S = 39 - 7.8
S = 31.20
Sales price is $31.20 Note: Always give monetary values to the nearest cent (or 1/100 decimal place).
If you performed the calculations with me, don't you find steps 2 and 3 a bit annoying? Try my short-cut
S = 39 - (20/100)*39
S = 39*(1 - 0.2)
S = 39*(0.8) Note: you don't have to subtract 7.8 from 39
S = 31.20
I tell my students to do 100 of this type of problem and rest assured they know how to do them. You can too! Good doing!
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