Answer:
1
Step-by-step explanation:
Let the number be n.
We are given:
n/12=q1+(7/12) where q1 is the quotient
n/6=q2+(?/6) where q2 is the quotient and ? is the remainder value we are trying to find.
? must be a integer between 0 and 5, inclusive. A remainder cannot be bigger than or equal to the divisor.
Let's rewrite the first equations
Multiply equation 1 on both sides by 2:
n/6=2q1+7/6
Remainder cannot be 7.
Rewrite again.
6 goes into 7 1 time with remainder 1.
n/6=2q1+(1+1/6)
n/6=(2q1+1)+1/6
So q2=2q1+1 and the remainder is 1 when dividing n by 6.
For fun. What is a number n with such conditions on it?
So what number has remainder 7 when divided by 12 and a remainder 1 when divided by 6.
n=12q1+7
n=6q2+1
If q1=1, we find a number right away that works.
19/12=1+7/12
19/6=3+1/6
