Q:

# A dinner was held to raise money for a children’smuseum. A ticket for one person cost $200 and aticket for a couple (two people) cost$350. A total of130 people attended the dinner, and the ticket salestotal was \$24,000. What is the total number of ticketsthat were sold?

Accepted Solution

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