Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total ticket receipts were $1950. Three-fourths as many teenagers as children attended. How many adults attended?

a. 200

b. 150

c. 220

d. 316

C=children

t=teens

a=adults

2c+3t+5a=1950

c+t+c=570

t = (3/4) c

so

replace t with (3/4) c

2c + (9/4) c+5a=1950

4.25c+5a=1950

c + (3/4) c+a=570

1.75c+a=570

elimination

use

1.75c+a=570

4.5c+5a=1950

we should eliminate c so we can solve for a

tough

um, solve for t first

eliminate a

mulitply first equation by - 5 and add to 2nd

-8.75c-5a=-2850

4.5c+5a=1950 +

-4.25c+0a=-900

-4.25c=-900

divide both sides by - 4.25

c=200

sub back

1.75c+a=570

1.75 (200) + a=570

350+a=570

mins 350 both sides

a=220

220 adults

200 kids

150 teens

220 adults

C is the answer