A 2-column table with 5 rows. Column 1 is labeled Days to Set Up with entries 1.5, 3, 4.5, x, 7.5. Column 2 is labeled Number of Concerts with entries 1, 2, 3, 4, 5. Stage hands set up a new stage for a concert in the arena every 1.5 days. Use proportional reasoning to find the value of x thatcompletes the table showing this relationship.

The relationship between two given variables can be expressed in the terms of proportion. These include direct proportion, inverse proportion, etc. When the proportional sign changes to equal to the sign, a constant of proportionality always exists.

Thus in the given question, it can be deduced that;

the number of days to set up is directly proportional to the number of concerts.

Such that;

number of days [tex]\alpha[/tex] number of concerts

number of days = k * number of concerts

where k is the constant of proportionality.

number of days = 1.5 * number of concerts

So, when the number of concerts is 1, then the number of days required to set up is 1.5.

Thus, when the number of concerts is 4, then;

number of days = 1.5*4

= 6.0

Therefore the number of days to set up when there are 4 concerts is 6.0 days.

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