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2 years ago

Which expression is equivalent to the expression shown ? 2 (x + 5) +3 (x2 - 5x +13)

1 answer:

3 0

$\text{Use the distributive property:}\\\\a(b+c)=ab+ac$

$2(x+5)+3(x^2-5x+13)=(2)(x)+(2)(5)+(3)(x^2)-(3)(5x)+(3)(13)\\\\=2x+10+3x^2-15x+39=3x^2-13x+49$

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Answer: 110 adult, 220 children and 75 senior citizens went to the theater that day.

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Let x represent the number of adults that went to the theater that day.

Let y represent the number of children that went to the theater that day.

Let z represent the number of senior citizens that went to the theater that day.

One day the theater sold 405 tickets. This means that

x + y + z = 405 - - - - - - - - - - - -1

movie theater charges $11.00 for adults, $6.50 for children, and $9.00 for senior citizens and the total number of receipts that were collected was $3315. This means that

11x + 6.5y + 9z = 3315 - - - - - - - - - -2

Twice as many children’s tickets were sold as adult tickets. This means that

y = 2x

Substituting y = 2x into equation 1 and equation 2, it becomes

x + 2x + z = 405

3x + z = 405 - - - - - - - - - - - - - 3

11x + 6.5 × 2x + 9z = 3315

11x + 13x + 9z = 3315

24x + 9z = 3315 - - - - - - - - - - -4

Multiplying equation 3 by 9 and equation 4 by 1, it becomes

27x + 9z = 3645

24x + 9z = 3315

Subtracting, it becomes

3x = 330

x = 330/3

x = 110

Substituting x = 110 into equation 3, it becomes

3 × 110 + z = 405

330 + z = 405

z = 405 - 330

z = 75

y = 2x = 2 × 110

y = 220

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