Question 1121102
<br>
Informally....<br>
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.<br>
Multiples of 4 that are multiples of 10, and less than or equal to 60, are 0, 20, 40, and 60.<br>
So the possible numbers of boxes of 4 is 0, 5, 10, or 15.<br>
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.<br>
Answer: the 2 possible values for x are 5 and 10.<br>
The same process, using the formal mathematical method....<br>
{{{4x+10y = 60}}}<br>
Solve for y:<br>
{{{10y = 60-4x}}}
{{{y = 6 - (2/5)x}}}<br>
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.<br>
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.