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DochEvi [55]
3 years ago
5

For a particular​ event, 669 tickets were sold for a total of ​$4293. If students paid ​$5 per ticket and nonstudents paid ​$8 p

er​ ticket, how many student tickets were​ sold?
Mathematics
1 answer:
solong [7]3 years ago
5 0

Answer:

353 tickets.

Step-by-step explanation:

Let's say that there are s student tickets and n nonstudent tickets.

s + n = 669

5s + 8n = 4293

Multiply -5 by the entire first equation to get...

-5s - 5n = -3345

Combine the two equations.

5s - 5s + 8n - 5n = 4293 - 3345

3n = 948

n = 316

Now, put the number of nonstudent tickets sold back into the first equation.

s + 316 = 669

s = 353 tickets.

Hope this helps!

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Read 2 more answers
Dana has 800 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed are
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Answer:

Perimeter of rectangle states that total distance around the outside, which can be found by adding together the length of each side.

As per the given statement, Dana has 800 yards of fencing to enclose a rectangular area.

Therefore, perimeter of rectangle = 800 yards.

Perimeter(P) of rectangle is given by :

P = 2(x+y) where x is the length and y is the width of the rectangles respectively.

Then,

2(x+y) = 800

Divide both sides by 2 we get;

x+y =400

or

y = 400 -x            .....[1]

We know, the area(A) of rectangle is given by

A = xy                   .....[2]

Substitute equation [1] into [2] we get;l

A = x(400-x)

using distributive property a\cdot (b+c) = a\cdot b+ a\cdot c

A = 400x -x^2            

or

A =-x^2+400x    ......[3]

To maximize the enclosed area.

For a quadratic function in standard form y =ax^2+bx+c , the axis of symmetry is a vertical line given by;  

x = -\frac{b}{2a}

Then; we have from equation [3]

a = -1 and b = 400

By axis of symmetry;

x = -\frac{b}{2a} = -\frac{400}{2 \cdot -1} =\frac{400}{2} = 200

Substitute in equation [1] to solve for y:

y = 400 - 200 = 200

The dimensions of the rectangle that maximize enclosed area are:

x = 200 units and y = 200 units.

Maximum area = 200 \times 200 = 40,000 square units.

We can say that maximum area of rectangle will always be a square



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