a. The moduli are coprime, so you can apply the Chinese remainder theorem directly. Let
- Taken mod 3, the last two terms vanish, and
so we need to multiply by the inverse of 2 modulo 3 to end up with a remainder of 1. Since 
, we multiply the first term by 2.
- Taken mod 4, the first and last terms vanish, and
. Multiply by the inverse of 3 modulo 4 (which is 3 because 
), then by 2 to ensure the proper remainder is left.
- Taken mod 5, the first two terms vanish, and
. Multiply by the inverse of 2 modulo 5 (3, since 
) and again by 3.
By the CRT, we have
i.e. any number 
(where 
is an integer) satisifes the system.
b. The moduli are not coprime, so we need to check for possible contradictions. If 
and 
, then we need to have 
. This basically amounts to checking that if , then we should also have 
.
The last congruence conflicts with the previous one modulo 3, so there is no solution to this system.
Answer:
5, assuming you get the worst possible slips off: 0,1,2,3,4
Step-by-step explanation:
Answer: 48 model cars
Step-by-step explanation: 1. You know that the ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 4:3.
2. Let's call the number of model cars that Jim owns is , therefore, you can solve the exercise as following:
3. Therefore, Jims owns 48 model cars.
