SOLUTION: Bod wants to put his footballs into boxes.
If he uses big boxes, he can put 7 footballs in each box with 4 footballs left over.
If he uses small boxes, he can put 5 footballs in
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If he uses big boxes, he can put 7 footballs in each box with 4 footballs left over.
If he uses small boxes, he can put 5 footballs in
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Question 1205528: Bod wants to put his footballs into boxes.
If he uses big boxes, he can put 7 footballs in each box with 4 footballs left over.
If he uses small boxes, he can put 5 footballs in each box with 4 footballs left over.
What is the smallest number of footballs that Bob could own? Found 2 solutions by Edwin McCravy, greenestamps:Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website! Bod wants to put his footballs into boxes.
If he uses big boxes, he can put 7 footballs in each box with 4 footballs
left over.
If he uses small boxes, he can put 5 footballs in each box with 4 footballs
left over.
What is the smallest number of footballs that Bob could own?
If he uses B big boxes, then he has 7B + 4 footballs.
If he uses S small boxes, then he has 5S + 4 footballs.
S small boxes.
Then he has 7B + 4 and also 5S + 4 footballs
The smallest number of footballs is when B and S are the smallest
they can be and be whole numbers.
That's when B=5 and S=7
So he has 7B+4 = 7(5)+4 = 35+4 = 39 footballs.
Checking:
It's also when he has 5S+4 = 5(7)+4 = 35+4 = 39 footballs.
Edwin
The number of footballs is 4 more than a multiple of 7 and also 4 more than a multiple of 5. Since 5 and 7 are relatively prime, the number of footballs is 4 more than a multiple of 7*5=35.
The smallest number that is 4 more than a multiple of 35 is 35(1)+4 = 35+4=39.
That of course does not consider the absurd case where the number of footballs is 35(0)+4 = 4.
