# Thread: 2 hard word problems

1. ## 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 $30 note? 2. A certain positive integer X greater than 100 is displayed. But when its two rightmost digits are erased, the number left is X/154. Find all possible numbers of X. 2. Hello, delicate_tears! Maybe I'm reading it wrong, but I don't understand #1 . . . 2. A certain positive integer$\displaystyle X$greater than 100 is displayed. But when its two rightmost digits are erased, the number left is$\displaystyle \frac{X}{154}.$Find all possible values of$\displaystyle X$. We have the number: .$\displaystyle X \;=\;"abc" \;=\;100a + 10b + c$. . where$\displaystyle b\text{ and }c$are digits . . . and$\displaystyle a$is any positive integer. If the two rightmost digits are erased, the number becomes: .$\displaystyle a$. . which equals$\displaystyle \frac{X}{154}$So we have: .$\displaystyle a \;=\;\frac{100a + 10b + c}{154} \quad\Rightarrow\quad 54a \:=\:10b + c$Since$\displaystyle 10b + c$is a two-digit number, the only solution is: .$\displaystyle a = 1,\:b = 5,\:c = 4$Therefore: .$\displaystyle X \;=\;154$3. Hi Delicate_Tears, 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.