It's 9 4/5 miles from Justin's house to the art museum the distance to the history museum is 9/10 this far
2 answers:
Answer:
<h2>The history museum has less distance from Justin's house, exactly there are 0.90 miles.</h2>Step-by-step explanation:
Givens
- From Justin's house to the art museum there are 9 4/5 miles distance.
- To the history museum is 9/10 miles.
First, we need to transform the mixed number into a fraction. We do this by mulitiplying the whole part with the denominator and then we sum with the numerator, as follows
Which means the distance between Justin's house and the art museum is 49/5 miles.
As you can observe , 49/5 miles > 9/10 miles, which means the history museum has less distance from Justin's house, exactly there are 0.90 miles.
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
Taken mod 4, the last two terms vanish and we're left with
We have , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with .
By the Chinese remainder theorem, we find that any such that
is a solution to this system, i.e. for any integer
, the smallest and positive of which is 149.