A promoter needs to make 63200 from the sale of 1300 tickets

A promoter needs to make $63,200 from the sale of 1300 tickets. She charges $44 for some tickets and $59 for the others.

(a) If there are x of the $44 tickets sold and y of the $59 tickets sold, write an equation that states that the sum of the tickets sold is 1300.

(b) Write an equation that states that the total amount received from the sale is $63,200.

(c) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $63,200.

please show work

Solution

a. x+y=1300
b. 44x
c.59y
d. 44x + 59y = 63200

x= number of $44 tickets
y= number of $59 tickets

1 x + 1 y = 1,300 .............1
Total value

44 x + 59 y = 63,200 .............2
Eliminate y
multiply (1)by -59
Multiply (2) by 1
-59 x -59 y = -76,700
44 x + 59 y = 63,200
Add the two equations
-15 x = -13,500
x = 900
plug value of x in (1)
1 x + 1 y = 1,300

900 + y = 1,300
y = 1,300 - 900
y = 400
y = 400
x= 900 number of $44 tickets
y= 400 number of $59 tickets