The Discounted Purchases : Puzzle

Until last week, Mandy had been putting off the purchase of four major items for her home, waiting for her town's annual bargain days. Each year, the town's four main stores (including Nickels) each send out a coupon for a different percentage discount (10%, 15%, 20%, or 30%) on the purchase of a single item. Can you find the discount that Mandy received on each of her buys, and determine from which store she purchased each item?

Given:

Discounts      : 10%, 15%, 20%, 30%
Store Names : Stears, Pal-Mart, Nickels, Dullard's
Appliances    : Computer, Dishwasher, Lawnmower, VCR

Clues:

1) The percentage discount Mandy received on her new computer was twice that of the item she bought at Dullard's. 

2) The discount on the Stears purchase was ten percentage points lower than the one on the riding lawnmower. 

3) The discount on the dishwasher wasn't 15%. 

4) Pal-Mart, (which didn't issue the 30% off coupon) isn't the store at which Mandy purchased the VCR.

Click here for SOLUTION!

The Discounted Purchases Puzzle : Solution

What was the challenge?

First let's have a given data.

Given:

Discounts: 10%, 15%, 20%, 30%
Store Names: Stears, Pal-Mart, Nickels, Dullard's
Appliances: Computer, Dishwasher, Lawnmower, VCR

Clues:

1) The percentage discount Mandy received on her new computer was twice that of the item she bought at Dullard's. 

2) The discount on the Stears purchase was ten percentage points lower than the one on the riding lawnmower. 

3) The discount on the dishwasher wasn't 15%. 

4) Pal-Mart, (which didn't issue the 30% off coupon) isn't the store at which Mandy purchased the VCR. 

 STEPS : 

1] As per clue (1), Dullard's didn't sell computer to Mandy and she didn't receive 10% or 15% off on computer. Also, Dullard's didn't offer her 20% or 30%.

2] The clue (2) suggests that the lawnmower wasn't purchased at 10% or 15% discount. Also, Stears discount must be 10% or 20%. And Stear didn't sell lawnmower for sure.

3] The clue (3) suggests that dishwasher wasn't sold at 15% discount. So, it's clear that Stears must have sold dishwasher at 10%/20% discount and Dullard's must have sold VCR at 15% discount. Therefore, computer must had been bought with 30% discount.

4] And hence, lawnmower at 20%. With that, Stears must have sold dishwasher at 10% discount as per clue (3).

5] Finally, as per clue (4), Pal-Mart didn't offer 30% discount suggests that it must not have sold computer. Therefore, Nickels sold computer at 30% discount and Pal-Mart sold lawnmower at 20% discount.

CONCLUSION : 

Final summary of the all purchases in form of table looks as - 

The Lossless Mistake

Bob buys two things in a shop. With his pocket calculator he calculates in advance what he has to pay: 5.25 dollars. But what he does not notice is that he pressed the division instead of the addition button. At the desk he is not surprised if he hears that he has to pay 5.25 dollars. 

What is the price of the two things Bob has bought?

Know the cost of those 2 things.

For Mistake To Be Lossless...

What was the mistake?

Let's assume that those things costs a and b respectively.

As per Bob's wrong calculation,

a / b = 5.25

a = 5.25 b  ..........(1)

And according to what should have been correct,

a + b = 5.25

Putting (1) in above,

5.25b + b  = 5.25

6.25b = 5.25

b = 0.84

Again putting this value in (1) gives,

a + 0.84 = 5.25

a = 5.25 - 0.84

a = 4.41

 
Hence the cost of 2 things are $4.41 and $0.84.

A Mathematical Buy!

In a classic wine shop in Flobecq, Belgium, list of three most popular wines are:

- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$

Homer Simpson entered the wine shop and he needs to buy

- All three types of wine shop.
- Needs to buy Dutch wine bottles in multiple of 20.
- Need to buy 100 wine bottles

Simpson has only 10000$. How many wine bottle(s) of each type, Simpson must buy? 

Simpson must buy.......Read More.... 

Source 
 

A Buy To Be Mathematical...

What was needed to buy?

Let's recollect the data where cost of each kind of wine bottle is listed.

- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$ (Cost of 1 bottle = 5$)

 

Now let F be the number of French bottle, G be the number of German bottles and D be the number of Dutch bottle that Simpson should buy.

F + G + D = 100

G = 100 - F - D   .....(1)

Total cost of all bottle must be $10000.

500F + 100G + 5D = 10000

Substituting (1) in above,

500F + 100(100 - F - D) + 5D = 10000

500F + 10000 - 100F - 100D + 5D = 10000

400F - 95D = 0

400F = 95D 
 
80F = 19D

D/F = 80/19

Possible values of D and F are 80 and 19 respectively.

From (1),

G = 100 - 19 - 80 =  1.

Let's verify if all these fits in his budget or not.  

19 French wine bottles would cost 19 x 500 = 9500, 1 German wine would cost = 1 x 100 = 100 and 80 Dutch wine bottles would cost 80 x 5 = 400. Remember we have got number of Dutch bottles in multiple of 20. Hence total cost = 9500 + 100 + 400 = 10000.

Hence with $10000, Simpson should buy 19 French, 1 German and 80 Dutch wine bottles if conditions of buying 100 bottles & Dutch bottles in multiple of 20 are applied.