Respuesta :
the answer would be C. i do believe hope this helps
The number of adults that attend the concert is given analyzing the given
information using simultaneous equation.
The number of adults that attended the concert is C. 220
Reasons:
The known parameters are;
The cost for children = $2.00
Cost for teenagers = $3.00
Cost for adults = $5.00
The number of people that attend the concert = 570
The total ticket receipts = $1,950
Number of teenagers attending the concert = Three-fourth the number pf children
Required:
Number of adults attending the concert
Solution:
Let c represent the number of children attending the concert, let t
represent the number of teenagers attending the concert, and let a
represent the number of adult attending, we have;
[tex]t = \dfrac{3}{4} \cdot c[/tex]...(1)
a + t + c = 570...(2)
5·a + 3·t + 2·c = 1,950...(3)
Plugging in the value of t from equation (1) in equation (2) and (3) gives;
[tex]a + \dfrac{3}{4} \cdot c + c = 570[/tex]
[tex]5 \cdot a + 3 \times \dfrac{3}{4} \cdot c + 2 \cdot c = 1,950[/tex]
Which gives;
[tex]5 \cdot a + \dfrac{17 \cdot c}{4} = 1950[/tex]...(4)
[tex]a + \dfrac{7 \cdot c}{4} = 570[/tex]...(5)
Multiplying equation (5) by 5 and subtracting equation (4) from it gives;
Therefore, we have;
[tex]5 \times \left(a + \dfrac{7 \cdot c}{4} \right) - 5 \cdot a + \dfrac{17 \cdot c}{4} = 5 \times 570 - 1950 = 900[/tex]
[tex]5 \times \left(a + \dfrac{7 \cdot c}{4} \right) - 5 \cdot a + \dfrac{17 \cdot c}{4} = \dfrac{9 \cdot c}{2}[/tex]
Therefore;
[tex]\dfrac{9 \cdot c}{2} = 900[/tex]
c = 200
Number of children, c = 200
Number of teenagers, t = (3/4) × 200 = 150
Number of adults, a = 570 - 200 - 150 = 220
The number of adults that attended is C. 220
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