A two digits number is such that four times the unit digit is five times greater than the tens digit. When the digits are reversed, the number is increased by nine. Find the number?

Answer 1

The probability of three independent events are 1/2,1/3,1/4 respectively. What's the probability that two of them will occur

Answer 2

4u=5t
10u+t = 10t+u + 9

now just solve for t and u

Answer 3

For the original number let the unit digit be x and the tens digit by y
so the number is 10y + x
so the number reversed will be 10x + y , which is now 9 more than the original, so
10x + y - (10y + x) = 9
9x - 9y = 9
x - y = 1

also 4x = 5y ---> x = 5y/4
using substitution:
5y/4 - y = 1
5y - 4y = 4
y =4, then x = 5(4)/4 = 5

So the original number is 45

check: number reversed is 54, is this greater by 9? YES
4 times the unit digit ----> 20
5 times the tens digit ----> 20

ok then!! 1/2,1/3,1/4

2nd problem:
2 of the 3 events to happen--> 1st and 2nd, 2nd and 3rd, 1st and 3rd
prob = (1/2)(1/3) + (1/3)(1/4) + (1/2)(1/4)
= 1/6 + 1/12 + 1/8
= 3/8