Linear or nonlinear: why?
2 answers:
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Answer:
The number of deserters is 34.
Step-by-step explanation:
We have to calculate the number of desertors in a group of 1500 soldiers.
The sergeant divides in groups of different numbers and count the lefts over.
If he divide in groups of 5, he has on left over. The amount of soldiers grouped has to end in 5 or 0, so the total amount of soldiers has to end in 1 or 6.
If he divide in groups of 7, there are three left over. If we take 3, the number of soldiers gruoped in 7 has to end in 8 or 3. The only numbers bigger than 1400 that end in 8 or 3 and have 7 as common divider are 1428 and 1463.
If we add the 3 soldiers left over, we have 1431 and 1466 as the only possible amount of soldiers applying to the two conditions stated until now.
If he divide in groups of 11, there are three left over. We can test with the 2 numbers we stay:
As only 1466 gives a possible result (no decimals), this is the amount of soldiers left.
The deserters are 34:
Recall your d = rt, distance = rate * time
the rate going south is 13, the rate going east is 10
it took a total amount of 6hours and 72miles for the whole travel
so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles
so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours
thus
solve for "t"
so, it travelled East for 6-t hours
the rate going south is 13, the rate going east is 10
it took a total amount of 6hours and 72miles for the whole travel
so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles
so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours
thus
solve for "t"
so, it travelled East for 6-t hours