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Brut [27]
3 years ago
6

Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t

icket receipts were $1950. Compared to the number of children in attendance, three-fourths as many teenagers attended. How many teenagers attended?
a. 200
c. 220
b. 150
d. 316
Mathematics
2 answers:
SIZIF [17.4K]3 years ago
8 0

Answer: b 150

Step-by-step explanation:

-Dominant- [34]3 years ago
4 0

Let

x--------> the number of children

y------> the number of teenagers

z------> the number of adults

we know that

2x+3y+5z=1,950 ------> equation A

x+y+z=570 -----> equation B

y=\frac{3}{4}x

x=\frac{4}{3}y -------> equation C

Substitute equation C in equation A and equation B

2[\frac{4}{3}y]+3y+5z=1,950

\frac{17}{3}y+5z=1,950 --------> equation D

[\frac{4}{3}y]+y+z=570

\frac{7}{3}y+z=570 --------> equation E

Multiply equation E by -5

-\frac{35}{3}y-5z=-2,850 --------> equation F

Adds equation D and equation F

\frac{17}{3}y+5z=1,950\\\\-\frac{35}{3}y-5z=-2,850\\\\---------\\\\-\frac{18}{3}y=-900\\\\y=3*900/18\\\\y=150\ teenagers

therefore

<u>the answer is the option</u>

150\ teenagers


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