jacob7542
14.04.2021 •
Mathematics
What is the value of x,y,z?plz help
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Ответ:
249335 miles
Step-by-step explanation:
Let x be the number of miles the car has travelled.
The odometer can only tell us that x≡49335(mod 100000).
If we also know the value of c where x≡c(mod 7)and 0≤c<7 by the Chinese remainder theorem we know the congruence satisfied by x modulo 100000•7 = 700000.
As long as the car has been driven less that 700000 this uniquely determines the number of miles driven.
In particular, we easily see that if x≡6 (mod 7)then the car was driven 49335 miles, if x≡4 (mod 7)then the car was driven 149335 miles, and if x≡2 (mod 7)then the car was driven 249335 miles