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3 years ago

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MATH HELP PLEASE !!!! Tickets to a local movie were sold at $5.00 for adults and $3.00 for students. If 150 tickets were sold fo

r a total of $610.00, how many adult tickets and student tickets were sold.

1 answer:

Vaselesa [24]3 years ago

3 0

Answer:

A = 80 S =70

Step-by-step explanation:

#Adults tickets = A

#Students tickets = S

A + S = 150

5A (means the price is $5 times the number of Adult tickets) equals the total amount for all of the Adult tickets altogether

3S (means the price is $3 times the number of Student tickets) equals the total amount for all of the students tickets altogether

5A + 3S = 610 (Means adding the total of all the student tickets plus adult tickets will equal $610 for all tickets sold)

Using both equations now, you can use substitution or elimination to solve for one of the variables. Then you can use the variable to substitute to solve the remaining one.

A + S = 150

5A + 3S = 610

Substitution:

A = 150 - S (Rearrange the first equation by moving S to the other side)

Substitute into the other equation

5 (150 - S) + 3S = 610

750 - 5S + 3S = 610 Combine like terms : -2S = -140

Solve for S = 70

Substitute into A + S = 150 A + (70) = 150

A = 80

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Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

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$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

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Distance is calculated as:

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So:

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$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

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$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

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Let

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$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

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$d' = \frac{du}{dx} * \frac{dd}{du}$

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$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

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Substitute: $u = x^2 - 5x +9$

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Split

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$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

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