Question

The amount of the tip each waiter receives after a wedding is inversely proportional to the number of waiters serving the event. If the total amount for tips at a wedding was $1,200 and n represents the number of waiters and t represents the tip received, which of these represents the relationship between n and t ?

a) n=t/ 1200
b) 1200=n/t
c) 1200=t/n
d) nt=1200

Answer 1

The relationship between n and t is n*t=1200 (option d)

Explanation:

Two quantities are inversely proportional if when multiplying (or dividing) one of them by a number, the other is divided (or multiplied) by the same number. That is, two magnitudes are inversely proportional if when one increases, the other decreases in the same proportion.

Given two variables, x and y, with an inversely proportional relationship, the product of both is always constant and equal to the coefficient of proportionality:

x*y=k

where k is the coefficient of proportionality.

This means that knowing the value of the proportionality coefficient and the value of a variable, the value of the other variable can be known through the quotient between the proportionality coefficient and the value of the known variable:

`y=(k)/(x)`

The amount of the tip "t" each waiter receives after a wedding is inversely proportional to the number of waiters "n" serving the event. The total amount for tips at a wedding was $1,200.Taking into account the aforementioned definition of inversely proportional quantities, this can be expressed by:

n*t=1200

The relationship between n and t is n*t=1200 (option d)