Final answer:
The ratio $42 for 81 juice boxes written as a simplified fraction is 14/27, after dividing both numerator and denominator by their common factor of 3.
Step-by-step explanation:
To write the ratio $42 for 81 juice boxes as a fraction, simply place the dollar amount over the number of juice boxes. So, the fraction is $42/81. To simplify this fraction, look for a common factor that you can divide both the numerator and the denominator by. In this case, both numbers are divisible by 3. Dividing the numerator ($42) and the denominator (81) by 3 gives us 14/27. Therefore, the simplified fraction representing the ratio of dollars to juice boxes is 14/27.