Name: nick

Who is asking: Student
Level: Secondary

Question:
hi,
actually i had cracked my brain for a long time and couldn't find a solution to this.please help!

One day jim played poker with some of his friends and lost half his money.the number of dollars he had before the game was the same as the number of cents he had after the game, and the no of cents he had before the game was twice as much as the number of dollars he had after the game.how much money did he have before thegame???

Later that day jim met a friend Al on the street."hi al!Do u have any change on you al?""yes"

"Good!can u give me a change of a dollar?" "I am afraid not!"

"Then give me change of 50 cents.""I am sorry i cant."

"how about a change of a quarter?""not possible."

"a dime."

"also not"

"a nickel?"

"not even that."

al had no bills or silver dollars on him.whats the largest amount of cash he could have had? hope u can help me.

thanking u in anticipation.

Hi Nick,
Suppose that Jim started with D dollars and C cents and after the game he had Da dollars and Ca cents. Thus when he started the value of his money in cents was 100 D + C. After the game the value of his money in cents was 100 Da + Ca.

You are given three facts

- 100 Da + Ca =
^{1}/_{2} (100 D + C)

- D = Ca

- C = 2 Da

Substituting the second two equations into the first gives

100 Da + Ca = ^{1}/_{2} (100 Ca + 2 Da)
which simplifies to
49 Ca = 99 Da
A crutial fact at this point is that Ca and Da are positive integers. Since 99 = 3^{2} x 11 divides the right side of the equation above it must divide the left side. Neither 3 nor 11 divide 49 and hence 99 = 3^{2} x 11 divides Ca. But Ca is the number of cents Jim has after the game so Ca is less than 100. Thus Ca = 99 and thus Da = 49. Make sure that you check that these values satisify the conditions given.

For the second problem start with pennies. Al can have at most 4 or he would have change for a nickle. For pennies he can not have 2 so he must have no nickles or 1 nickle. If he has one nickle how many dimes can he have? If he has no nickles how many dimes can he have? In each case what about quarters? What about half-dollars?

I hope this helps,

Penny