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25 January, 08:13

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

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Answers (1)
  1. 25 January, 08:26
    0
    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
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