Tickets for a children's musical cost 3.50 for adults and 2.00 for children. if 250 tickets were sold for a total of 650.00 how many tickets of each kind were sold

Number of adult tickets sold is 100 and number of children tickets sold is 150

Solution:

Let "c" be the number of childrens ticket sold

Let "a" be the number of adult tickets sold

Cost of 1 children's musical ticket = $ 2.00

Cost of 1 adult musical ticket = $ 3.50

Given that 250 tickets were sold

number of childrens ticket sold + number of adult tickets sold = 250

c + a = 250 ---- eqn 1

250 tickets were sold for a total of 650

So we can frame a equation as:

number of childrens ticket sold x Cost of 1 children's musical ticket + number of adult tickets sold x Cost of 1 adult musical ticket = 650

2c + 3.50a = 650 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn 1,

c = 250 - a ----- eqn 3

Substitute eqn 3 in eqn 2

2(250 - a) + 3.50a = 650

500 - 2a + 3.50a = 650

1.5a = 150

From eqn 1,

c = 250 - 100

Thus number of adult tickets sold is 100 and number of children tickets sold is 150

they would have to work 32 hours.