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Novosadov [1.4K]
3 years ago
5

The City Zoo has different admission prices for children and adults. When three adults and two children went to the zoo, the pri

ce was $81.22. If two adults and three children got in for $77.18, then what is the price of an adult's ticket and what is the price of a child's ticket?
Mathematics
1 answer:
Strike441 [17]3 years ago
4 0

Let the price of a children's ticket be x and the price of an adult's ticket be y. We can form a system of equations to solve this problem.


2x + 3y = 81.22

3x + 2y = 77.18


Lets use elimination to solve the system. First, lets multiply the first equation by 3 and the second equation by 2 so the x terms will cancel out.


6x + 9y = 243.66

6x + 4y = 154.36


We can then subtract the equations to cancel out the x variable.


6x + 9y = 243.66

-(6x + 4y = 154.36)

(6x-6x) + (9y - 4y) = (243.66 - 154.36)

0 + 5y = 89.30


Finally, we can find the value of y.


5y = 89.30

y = 17.86


Lastly, we can plug in the value of y and solve for x to find the value of the child's ticket.


2x + 3(17.86) = 81.22

2x + 53.58 = 81.22

2x = 27.64

x = 13.82


Therefore, the child ticket costs $13.82 and the adult ticket costs $17.86.

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The length of a rectangle board is 10 centimeters longer than its width. The width of the board is 26 centimeters. The board is
Troyanec [42]

Answer:

Area of each piece = 104 cm^{2}

Possible dimensions are 26 cm by 4 cm, 13 cm by 8 cm.

Step-by-step explanation:

Given that:

Dimensions of the rectangular board as:

Length of the board is 10 cm longer than its width.

Width of the board = 26 cm

Length of the board = 26 + 10 = 36 cm

The rectangular board is divided into 9 equal pieces.

To find:

Area of each piece and

the possible dimensions of each piece = ?

Solution:

First of all, let us calculate the area of bigger rectangular board.

Area of a rectangle is given by the following formula:

Area = Length \times Width

Area = 26 \times 36 cm^2

Area of each smaller rectangle = \frac{26\times 36}{9} = 104\ cm^2

To find the possible dimensions, we need to find the factors of 104.

104 = 26 \times 4

104 = 13 \times  8

Therefore, the Possible dimensions are 26 cm by 4 cm

and

13 cm by 8 cm.

5 0
3 years ago
Tommy opens an account with $50 and deposits $10 a week. The same week, Shelby opens an account with $25 and adds $10 a week. ho
asambeis [7]
There is no solution since they are both adding $10 to their accounts every week.
6 0
2 years ago
At 10:30am,a submarine was 43 feet below the ocean surface.By10:45am,it was 271 feet below the surface. How much did it descend
matrenka [14]

Hi!

Your answer would be:<em> 228ft below the ocean surface.</em>

Reason being: <em>when you subtract 43 from 271, you get 228.</em>

Hope this helps!

If you need anymore help, please let me know!

<em>Yours Truly,</em>

<h2><em>~~~PicklePoppers~~~</em></h2>
4 0
3 years ago
Which of the following functions are solutions of the differential equation y+4y+4y=0? A. y(x) =e^-2x B. y(x) = e^+22 C. y(x) =
zmey [24]

Answer: E. y(x) = 0

Step-by-step explanation:

y(x) = 0 is the only answer from the options that satisfies the differential equal y" - 4y' + 4y = 0

See:

Suppose y = e^(-2x)

Differentiate y once to have

y' = -2e^(-2x)

Differentiate the 2nd time to have

y" = 4e^(-2x)

Now substitute the values of y, y', and y" into the give differential equation, we have

4e^(-2x) - 4[-2e^(-2x)] + 4e^(-2x)

= 4e^(-2x) + 8e^(-2x) + 4e^(-2x)

= 16e^(-2x)

≠ 0

Whereas we need a solution that makes the differential equation to be equal to 0.

If you test for the remaining results, the only one that gives 0 is 0 itself, and that makes it the only possible solution from the options.

It is worth mentioning that apart from the trivial solution, 0, there is a nontrivial solution, but isn't required here.

7 0
3 years ago
The solutions to the equation f(x) = g(x) are -2 and 1. Iff and g are graphed on the same coordinate plane, which statement must
Oksanka [162]

Answer:

The correct option is;

The function will intersect at x = -2 and x = 1

Step-by-step explanation:

The question parameters are

The functions in the question are f(x) and g(x)

The solution to the equation f(x) = g(x) are -2, and 1

Given that the equations, f(x) and g(x), are both given in values of x, their solution will be the x values that satisfies both functions

Therefore, the functions will intersect (have the same values of f(x) and g(x)) at the points of the solutions, which are given as x = -2, and x = 1

6 0
3 years ago
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