Stupidly simple, yet confusing (For me) sales problem

What is the difference, please explain..!!

A pair of shoes is normally priced at $37. What will be the sale price if a 25% sales discount is offered?

I would assume i reduce $37 by 25%, i.e 37/1.25 = $29.60

However the answer is $37 x 0.75 = $27.75.

What is the difference in arising to the two unique solutions?

Re: Stupidly simple, yet confusing (For me) sales problem

To reduce a quantity $\displaystyle A$ by 25%, you need to take 100% of $\displaystyle A$ minus 25%.

$\displaystyle (1-0.25)A = 0.75A $

By dividing by 125%, you're really reducing the quantity by 20%.

$\displaystyle \frac{1}{1.25}A = 0.8A = (1 - 0.20)A $

Re: Stupidly simple, yet confusing (For me) sales problem

Quote:

Originally Posted by

**audusdyengbp** I would assume i reduce $37 by 25%, i.e 37/1.25 = $29.60

That's a very neat way of reversing a 25% increase.

You probably learnt it long ago in a lesson that was all about the difference you're asking about here, i.e. the very big difference between reducing by 25% and reversing a 25% increase.

Funny thing is, reversing should be the trickier of the two, but you've 'over-learnt' it, and are applying it regardless, just like most people (before that lesson) try to reverse a 25% increase by reducing by 25%.

So you need to get back in touch with the more obvious intuition. I suggest the following.

Think of the $37 as a tower of 4 bricks. You've been asked to remove the top one.

What you tried was a way of removing a fifth brick placed on the top.

Re: Stupidly simple, yet confusing (For me) sales problem

Quote:

Originally Posted by

**JohnDMalcolm** To reduce a quantity $\displaystyle A$ by 25%, you need to take 100% of $\displaystyle A$ minus 25%.

$\displaystyle (1-0.25)A = 0.75A $

By dividing by 125%, you're really reducing the quantity by 20%.

$\displaystyle \frac{1}{1.25}A = 0.8A = (1 - 0.20)A $

now this makes sense.

the reason i did 37/1.25 to reduce by 25% is due to my financial instruments class where we have to discount a bond value back to its present value.

i.e if the future value of a bond 1 year from now is $1000, and interest rates are currently 5% then the present value is the future value DISCOUNTED back to one period at the interest rate, being 1000/1.05.

thank you.

if anyone can offer any more clarification, it would be appreciated.

Re: Stupidly simple, yet confusing (For me) sales problem

Quote:

Originally Posted by

**tom@ballooncalculus** That's a very neat way of reversing a 25% increase.

You probably learnt it long ago in a lesson that was all about the difference you're asking about here, i.e. the very big difference between reducing by 25% and reversing a 25% increase.

Funny thing is, reversing should be the trickier of the two, but you've 'over-learnt' it, and are applying it regardless, just like most people (before that lesson) try to reverse a 25% increase by reducing by 25%.

So you need to get back in touch with the more obvious intuition. I suggest the following.

Think of the $37 as a tower of 4 bricks. You've been asked to remove the top one.

What you tried was a way of removing a fifth brick placed on the top.

actually im still confused.

lets look at it this way:

increasing $1000 by 25% is 1000 x 1.25 = $1250

now if we reduce $1250 by 25% again, are you saying it is $1250 x 0.75 = $937.50, and not $1250/1.25 = $1000?

Because $1250/1.25 is an 20% reduction (1/1.25 = 0.8).

this is correct?

EDIT:

so lets say i do add that 5th brick, then if i take 25% of the 5 brick structure, i get ((37 x 0.75 = 27.75).

Using this brick logic, how would you interpret 37/1.25 = 29.6 then?

Re: Stupidly simple, yet confusing (For me) sales problem

Quote:

Originally Posted by

**audusdyengbp** actually im still confused.

lets look at it this way:

increasing $1000 by 25% is 1000 x 1.25 = $1250

now if we reduce $1250 by 25% again, are you saying it is $1250 x 0.75 = $937.50, and not $1250/1.25 = $1000?

Because $1250/1.25 is an 20% reduction (1/1.25 = 0.8).

this is correct?

Yes! Totally.

Quote:

Originally Posted by

**audusdyengbp** EDIT:

so lets say i do add that 5th brick, then if i take 25% of the 5 brick structure, i get ((37 x 0.75 = 27.75).

Although you can't do this without sawing into one of the bricks. Embarking on a 25% reduction in the first place should tell you to look at the given amount as a tower of 4 not 5.

Quote:

Originally Posted by

**audusdyengbp** Using this brick logic, how would you interpret 37/1.25 = 29.6 then?

As removing one of 5 bricks.

Or as reducing by 20%.

Or as dividing by five quarters (which would reverse a multiplication by five quarters which is an increase by one quarter).

Re: Stupidly simple, yet confusing (For me) sales problem

Quote:

Originally Posted by

**tom@ballooncalculus** Yes! Totally.

Although you can't do this without sawing into one of the bricks. Embarking on a 25% reduction in the first place should tell you to look at the given amount as a tower of 4 not 5.

As removing one of 5 bricks.

Or as reducing by 20%.

Or as dividing by five quarters (which would reverse a multiplication by five quarters which is an increase by one quarter).

Tom, Mate - you are a legend!

Thanks :)