Let x be Luna's house rental budget.
The total budget for house and food rental is represented by the equation x + (60x/100) = 240.
The equation becomes 100x + 60x = 24000 after multiplying each term by 100 to get rid of the fraction.
By combining like terms, the equation becomes 160x = 24000.
Thus, the value of x is 24000/160 = <<24000/160=150>>150 which represents the house rental budget.
So, Luna's food budget is $240 - $150 = $<<240-150=90>>90.
Her phone bill budget is $90 x 10/100 = $<<90*10/100=9>>9.
Therefore, Luna's monthly budget for all those expenses is $240 (house and food) + $9 (phone) = $<<240+9=249>>249.
#### 249