Question

A concert promoter needs to make $42,800 from the sale of 1840 tickets. The promoter charges $20 for some tickets and $30 for the others, Let x represent the number of $20 tickets and y represent the number of $30 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 recelved from the sale of $20 tickets? (c) Write a formula for how much money is received from the sale of $30 tickets? (d) Write an equation that states that the total amount received from the sale is $42,800 (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $42,800.

Answer 1

Total number of tickets = 1840

a) x = $20 tickets.

y = $30 tickets.

so answer of part a) is x + y = 1840

b) 20*x = total money received by selling $20 tickets.

therefore answer of this part is 20*x

c) Similarly the answer of this part is  30*y

d) Total sale = 42800

20*x + 30*y = 42800  ( this is the answer of part d)

e) We get two equations as

x + y = 1840 ....( 1 ) and 20x + 30y = 42800 ....( 2 )

from equation ( 1 ), we get y = 1840 - x

Plug this value in equation ( 2 ), we get:

20x + 30(1840 - x ) = 42800

20x - 30x = 42800 - 55200 = -12400

-10x = -12400

x = 1240

plug this value in equation ( 1 ), we get:

1240 + y = 1840

y = 1840 - 1240 = 600

Therefore, x = 1240 and y = 600