SOLUTION: A grocery stores sells tomatoes in boxes of 4 or 10. If a shopper buys x boxes of 4 and y boxes of 10, where x ≥ 1 and y ≥ 1, for a total of 60 tomatoes, what is one

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Question 1121102: A grocery stores sells tomatoes in boxes of 4 or 10. If a shopper buys x boxes of 4 and y
boxes of 10, where x ≥ 1 and y ≥ 1, for a total of 60 tomatoes, what is one possible value of x?
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
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Clearly otherwise

So is bounded above and below by and restricted to the integers (no fractional boxes of 10 tomatoes).

In other words:

Test these values in to eliminate values of that do not result in integer values of


John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Informally....

The total number of tomatoes is a multiple of 10; and y boxes of 10 each will be a number of tomatoes that is a multiple of 10. Therefore, the total number of tomatoes in the boxes of 4 each must be a multiple of 10.

Multiples of 4 that are multiples of 10, and less than or equal to 60, are 0, 20, 40, and 60.

So the possible numbers of boxes of 4 is 0, 5, 10, or 15.

15 boxes of 4 each would mean 0 boxes of 10 each. Since the problem specifies having at least one box of each size, the possible numbers of boxes of 4 each are 5 and 10.

Answer: the 2 possible values for x are 5 and 10.

The same process, using the formal mathematical method....

4x%2B10y+=+60

Solve for y:

10y+=+60-4x
y+=+6+-+%282%2F5%29x

y must be a positive integer; and 6 is an integer. That means(2/5)x must be an integer; and that means x must be a multiple of 5.

The conditions of the problem say x must be a positive integer, and that the value of x must be less than 15. Since we have determined that it also must be a multiple of 5, the only 2 possible values of x are 5 and 10.