Answer:
Total Number of tickets sold is 90.
Step-by-step explanation:
Given:
Cost for 1 person ticket = [tex]\$200[/tex]
Cost for Couples ticket = [tex]\$350[/tex]
Let the number of 1 person attended dinner be [tex]x[/tex].
Also Let the number of Couples attended dinner be [tex]y[/tex]
Total number of people attended dinner = 130
[tex]x+2y=130 \ \ \ \ equation \ 1[/tex]
Now Ticket sale = [tex]\$24000[/tex]
Hence,
[tex]200x + 350y =24000\\[/tex]
Dividing both sides by 50 we get,
[tex]\frac{50(4x+7y)}{50}=\frac {24000}{50}\\4x+7y=480 \ \ \ \ \ equation \ 2[/tex]
Multiplying equation 1 by 4 we get,
[tex]x+2y=130 \\4(x+2y)=130 \times 4 \\4x+8y= 520 \ \ \ \ \ equation \ 3[/tex]
Subtracting equation 2 by equation 3 we get;
[tex](4x+8y= 520)-(4x+7y=480)\\y = 40[/tex]
Now Substituting value of y in equation 1 we get;
[tex]x+2y=130\\x+2\times 40 =130\\x+80 =130\\x =130-80\\x=50\\[/tex]
Hence total number of tickets sold = [tex]x+y =40 +50 =90[/tex]
Total Number of tickets sold is 90.
