MATH SOLVE

3 months ago

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 = [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.