Question

A concert promoter needs to make $85,600 from the sale of 1840 tickets. The promoter charges $40 for some tickets and $60 for the others. Let x represent the number of $40 tickets and y represent the number of $60 tickets. (a) Write an equation that states that the sum of the tickets sold is 1840. (b) Write a formula for how much money is received from the sale of $40 tickets? $ (c) Write a formula for how much money is received from the sale of $60 tickets? $ (d) Write an equation that states that the total amount received from the sale is $85,600. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $85,600. x = y =

Answer 1

According to the given data, we have the following ones.

(a) The equation that states that the sum of the tickets sold is 1840 is, x + y = 1840​​​​​​

.

(b) Money received from the sale of $40 tickets is $40x​​​​​​

.

(c) Money received from the sale of $60 tickets is $60y

.

(d) The equation that states that the total amount received from the sale is $85,600 is, 40x + 60y = 85600​​​​​​

.

(e) Now (40x + 60y) - 40(x + y) = 85600 - 40*1840

i.e. 40x + 60y - 40x - 40y = 85600 - 73600

i.e. 20y = 12000

i.e. y = 600

So, x = 1840 - 600 = 1240

So we have,

x = 1240​​​​​​

y = 600