Answer: Choice C) David should buy 5 packages of buns and 6 packages of hot dogs.
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Explanation:
Focus on the hot dog buns for now
1 package = 12 hot dog buns
2 packages = 24 hot dog buns (multiply both sides by 2)
3 packages = 36 hot dog buns (multiply original equation by 3)
We can see that the multiples of 12 are being listed. So we have
12, 24, 36, 48, 60, 72, 84, ...
as the possible number of hot dog buns we could get if we buy 1,2,3... packages.
The possible number of hot dogs we can get are
10, 20, 30, 40, 50, 60, 70, 80, ...
which are multiples of 10. Simply add 10 to each item to get the next one.
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Considering these two sets
12, 24, 36, 48, 60, 72, 84, ...
10, 20, 30, 40, 50, 60, 70, 80, ...
what is the lowest common multiple? That would be 60 since it is found in both lists and it is the smallest in common.
The LCM of 12 and 10 is 60.
If he wanted 60 hot dog buns, then 60/12 = 5 packages of buns is what he needs.
If he wanted 60 hot dogs, then he needs 60/10 = 6 packages of hot dogs.
Therefore, David should buy 5 packages of buns and 6 packages of hot dogs. The answer is choice C.
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Side note: a different way to find the LCM is to multiply 10 and 12 to get 10*12 = 120. Then we divide by the GCF 2 getting 120/2 = 60.
