Answer:
a) x + y = 3200... Equation 1
b) $72,500
c) $17,400
d) 25x + 58y = 89,900.... Equation 2
Explanation:
A promoter needs to make $89,900 from the sale of 3200 tickets. She charges $25 for some tickets and $58 for the others.
Hence, the system of Equations is given as:
Let the
Number of the $25 tickets sold = x
Number of the $58 tickets sold = y
Hence:
x + y = 3200... Equation 1
x = 3200 - y
$25 × x + $58 × y= $89,900
25x + 58y = 89,900..... Equation 2
Substitute 3200 - y for x
25(3200 - y ) + 58y = 89,900
80,000 - 25y + 58y = 89,900
- 25y + 58y = 89,900 - 80,000
33y = 9,900
y = 9,900/33
y = 300 tickets
Solving for x
x = 3200 - y
x = 3200 - 300
x = 2900 tickets
(a) If there are x of the $25 tickets sold and y of the $58 tickets sold, write an equation that states that the sum of the tickets sold is 3200.
x + y = 3200... Equation 1
(b) How much money is received for the sale of x tickets for $25 each?
x = 2900 tickets
Hence:
$25 × 2900 tickets
= $72,500
(c) How much money is received for the sale of y tickets for $58 each?
y = 300 tickets
Hence:
$58 × 300
= $17,400
(d) Write an equation that states that the total amount received from the sale is $89,900.
25x + 58y = 89,900.... Equation 2
(e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $89,900.