MATH SOLVE

3 months ago

Q:
# Tickets for the community fair cost $12 for adults and $5 dollars for children. On the first day of the fair, 312 tickets were sold for a total of $2,204 . How many adult tickets and how many child tickets were sold?

Accepted Solution

A:

With this information we can set up 2 equations:x + y = 312 (# of tickets sold for adults + # of tickets sold to adults = 312)12x + 5y = 2204 ( # of tickets sold for adults times $12 + # of tickets sold to adults times $5 = $2204)Where x is how many tickets were sold to adults and y how many tickets were sold to childrenNow we can solve this system of equations by substitution:isolate y in the first equation to find its value and plug it in the second equationx + y = 312isolate y by subtracting x from both sides:x - x + y = 312y = 312 - xApply y = 312 - x to the second equation12x + 5y = 220412x + 5( 312 - x) = 220412x + 1560 - 5x = 22047x + 1560 = 2204Subtract 1560 from both sides to isolate x7x + 1560 - 1560 = 2204 - 15607x = 644Divide both sides by 77/7x = 644/7x = 92Now plugin 92 for x in the first equation to find the value of yx + y = 31292 + y = 312subtract 92 from both sides92 - 92 + y = 312 - 92y = 220x = 92, y = 22092 tickets were sold to adults and 220 tickets were sold to childrenHope it helps :)Branliest would be appreciated