Who is asking: Student Level: Secondary
actually i had cracked my brain for a long time and couldn't find a solution to this.please help!
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
Substituting the second two equations into the first gives
A crutial fact at this point is that Ca and Da are positive integers. Since 99 = 32 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 = 32 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,