2 hard word problems
This is for a maths challenge thing I'm doing but I'm gonna change the numbers around a bit so that I'm not relying on others for help entirely. Please be really clear on the method and steps used- I know you guys are of great help but sometimes your understanding of maths just goes beyond my capabilties.
1. Person A needs a $30. ATMs dispenses either $30, $40 or $70 notes. What is the largest amount he can withdraw to be certain that he has at least one $30 note?
2. A certain positive integer X greater than 100 is displayed. But when its two rightmost digits are erased, the number left is X/154. Find all possible numbers of X.
Maybe I'm reading it wrong, but I don't understand #1 . . .
We have the number: .
. . where are digits . . . and is any positive integer.
If the two rightmost digits are erased, the number becomes: .
. . which equals
So we have: .
Since is a two-digit number, the only solution is: .
I can only imagine the solution to be $870. The Least Common Multiple of 30, 40, and 70 is $840. An ATM dispenser machine may give you $840 in bills of 30s only, 40s only, 70s only, or a mix between them. The only way to make sure that the bill has to give you a 30 dollar bill is to add 30 to the LCM.