I love these problems!
1) N=11 when divided by 12
So if you are familiar with modular arithmetic, we will write some equations.
N==2 (mod 3)
N==3 (mod 4)
Let's solve for N.
a and b are integers
take the whole thing modulo 3
so inputting for a new quotient integer c,
N= 11 (mod 12)
or the remainder is 11 when divided by 12
The GCF is 102.
Again, use modular arithmetic with integer variable quotients. Solving the way I did before, N=311 (mod 315) so N>=311+315n, and n can't be negative thus N=311.
4) 38 candies
lol, same modular arithmetic.
Solving equations and writing them, we have for the # of candies=x
so x=3(mod 35)
and x=6(mod 8)
therefore x= 38 mod 280, and x=38
(because 318 would obviously be too many candies for >8 people to eat.)
Yay, I love rate problems!
Noon is 12:00 PM.
So train A leaves at 12:00 PM and drives at 90 mph (I know right? CLASS 5 PASSENGER THAT'S LUXURY). And train B leaves from the same place and drives from the same direction at 10 mph greater than 90mph. In 30 minutes 12-12;30, Train A will go 45 miles and Train B will go 0 miles (Not left yet). In another 30 minutes, a total of 1 hour, Train A will have went 90 miles and train B will go 50. 2 hours, 180 miles VS 150 miles. 4 hours, 360 miles VS 350 miles. And 5 hours will add a total of 10 miles difference, which is 450 vs 450!!! Therefore 12:00+5:00=
17:00 in 24 hour clock
and 5:00 PM in 12 hour clock!
Note that all of these pizzas have cheese.
Subtract equations 2 from 3 and get Onions=$1.59.
Then you can't find out any more, as this is a pizza estimation problem that has too many variables and I don't eat pizza soooooo...
Square root 90 is 3 * sqrt 10. It is irrational and therefore not rational.
It is real because it is not a letter, it is a number.
It is not whole obviously,
natural is whole except no 0s so not natural.
Not an integer= all negative and positive and 0 counting numbers.
It is only irrational and Real.