[Guest]

Mr A amd Mr. B went for some shopping and bought 3 items each. By a coincidence, they both spent exaclty

$222.22. Mr. A observed something else- looking at the price of each item, the value in dollars is the square of the value

in cents.

If one of A's items cost $1.01 and one of B's item cost $169.13, what are the price of other itmes.

** I got the answer right but through Hit and Trial method. Can anyone guide me how to reach the answer logically?

[Guest]

Indeterminate case for 2 item prices for each Mr. A and Mr. B.

Mr. A 's items : 1.01, 25.05, 196.16

Mr B's Items: 169.13, 4.02, 49.07

[Guest]

Let's work it out for A. Since one of his items has cost of 1.01, remaining two will have together 221.21 (222.22-1.01). Now let's say cent's parts are 'a' cent and 'b' cent for those two items.

So, we have a+b = 21 or a+b = 121 (note that it cannot be 221 or higher as a,b <100).

Similarly from dollar's part we will have a^2+b^2 = 221 or a^2+b^2 = 220 respectively.

From first set of equation,

(a+b)^2 = 441 or 14641.

 a^2+b^2+2ab = 441 or 14641

 a^2+b^2+2ab – a^2+b^2 = 441-221 or 14641-220

 2ab = 220 or 14421

 a^2+b^2-2ab = 221-220 or 220-14421

 (a-b)^2 = 1 or -14201. Square can’t be negative. So we will take it as 1

 a-b = 1 or -1 but a+b = 21 in this case.

 (a,b) = (10,11)

 Prices are 100.10 and 121.11

By similar logic, for B, prices would be 49.07 and 4.02

[Guest]

Indeterminate case for 2 item prices for each Mr. A and Mr. B.

Mr. A 's items : 1.01, 25.05, 196.16

Mr B's Items: 169.13, 4.02, 49.07

16*16 = 256, not 196. 14*14 = 196

[Guest]

Mr A's Items = $1.01, $100.10 & $121.11

Mr B's Items = $ 4.02, $49.07 & $169.13

The Logic i used was i subtracted the amount of 1 item from the total amount (ie 222.22 - 1.01 = 221.21 & 222.22 - 169.13 = 53.09 )

For Mr A 's bill the outstanding amount for remaining 2 items was 221.21$. In this case we cant have the last 2 digits any above then 11cents otherwise it would exceed the total amount.

For Mr B 's bill the outstanding amount for remaining 2 items was 53.09$. In this case we cant have the last 2 digits any above then 07cents otherwise it would exceed the total amount.

once you have figured that out, there's nothing left to solve.

regards

Nick

[Guest]

Good..nak got it in post#2 and Swapnil got it with expalination in Post#3

[Guest]

lets say for case "A"

item 1+item2+item 3=222.22

item 1 +item2+1.01=222.22

item1 +item 2=221.21

now the wit

we know that the rate is like

X^2.X+Y^2.Y=221.21

so,

X^2+ Y^2=221

and

X+Y=21

and so now I think It's simple enough to be solved so I leave it up to you............and similarly we need to find the another one

[Guest]

Not to quibble, but "the value in dollars is the square of the value in cents" means that the whole value as expressed in dollars is equal to the whole value as expressed in cents. $169.13 would have to equal 16,913^2. The examples of item prices given helped clarify, but the question should have read "the value of whole dollars is the square of the remaining cents" or "the value on the left of the decimal point is the square of the value on the right"

[Guest]

Indeterminate case for 2 item prices for each Mr. A and Mr. B.

Mr. A 's items : 1.01, 25.05, 196.16

Mr B's Items: 169.13, 4.02, 49.07

Please keep this in mind 16 square is 256 not 196