The cost of a conference party for a group of participant is partly constant and partly varies inversely as the number of participant .if the cost of 850 when there are 17 participant and 550 when they are 11 participant, find the cost when there are 20 participant
To solve this problem, we can assume that the cost of the party, C, has two components: a constant cost, k, and a variable cost that varies inversely with the number of participants, p.
So, we can express this relationship using the formula: C = k + (c/p), where c is a constant.
Given that the cost is $850 when there are 17 participants, we can substitute these values into the equation and solve for k and c.
850 = k + (c/17) ------ Equation 1
Similarly, when there are 11 participants and the cost is $550, we can substitute these values into the equation.
550 = k + (c/11) ------ Equation 2
Now, let's solve these two equations to find the values of k and c.
First, we multiply Equation 1 by 11 and Equation 2 by 17 to eliminate the denominators:
11 * 850 = 11k + c
17 * 550 = 17k + c
Simplifying these equations:
9350 = 11k + c ------ Equation 3
9350 = 17k + c ------ Equation 4
Now, subtract Equation 4 from Equation 3 to eliminate c:
11k + c - (17k + c) = 9350 - 9350
11k - 17k = -0
-6k = 0
Dividing both sides of the equation by -6:
k = 0
Now, substitute the value of k back into one of the original equations, like Equation 1.
850 = 0 + (c/17)
Simplifying:
850 = c/17
Multiply both sides of the equation by 17:
850 * 17 = c
c = 14450
Therefore, the equation for the cost of the party is:
C = 0 + (14450/p)
To find the cost when there are 20 participants, substitute p = 20 into the equation:
C = 0 + (14450/20)
C = 0 + 722.5
Hence, the cost when there are 20 participants is $722.50.