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Step2247 [10]
3 years ago
9

There are 450 people at a play, the total receipt for $600 and the admission was $2 for adults and $0.75 for children, how many

adults and how many children were in attendance?
Mathematics
1 answer:
sdas [7]3 years ago
8 0

Answer:

340 children, 210 adults.

Step-by-step explanation:

Let \ a \ - adults, \ c - children;\\c + a = 450\\0.75c + 2a = 600|\cdot 4\\3c + 8a = 2400;\\\\c + a = 450|\cdot(-3)\\3c + 8a = 2400\\-3c -3a = -1350\\5a = 1050 => a = 210, c = 450 -210 = 340.

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Let x =  day number (1,2,3,4, ...)
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y = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Substitute x=1,2, ..., 5 into y(x) to obtain the matrix equation
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| 3⁴  3³  3²  3¹  3⁰   |  | a₃ |  =  | 61 |
| 4⁴  4³  4²  4¹  4⁰   |  | a₄ |      | 65 |
| 5⁴  5³  5²  5¹  5⁰  |  | a₅ |      | 56 |

When this matrix equation is solved in the calculator, we obtain
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a₂ =  -55.3333
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Test the solution.
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y(6) = 152
y(7) = 571
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