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Nikitich [7]
3 years ago
12

At the movie theatre, child admission is $5.30 and adult admission is $8.40. On Wednesday, three times as many adult tickets as

child tickets were sold, for a
total sales of $1189.50. How many child tickets were sold that day?
Mathematics
1 answer:
aleksley [76]3 years ago
6 0

Answer:

39

Step-by-step explanation:

Let x = number of child tickets sold.

Cost of x child tickets is x * 5.30 = 5.3x.

"three times as many adult tickets as child tickets were sold"

Number of adult tickets sold: 3x

Cost of 3x adult tickets is 3x * 8.40 = 25.2x

Cost of all tickets is 5.3x + 25.2x = 30.5x

Cost of all tickets is $1189.50

30.5x = 1189.5

x = 1189.5/30.5

x = 39

Answer: 39

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If x+y=12 and xy=15,find the value of (x^2+y^2)
Mice21 [21]

Answer:  x^2+y^2=\dfrac{105\pm 18\sqrt6}{2}

<u>Step-by-step explanation:</u>

EQ1:  x + y = 12     --> x = 12 - y

EQ2:  xy = 15      

Substitute x = 12-y into EQ2 to solve for y:

(12 - y)y = 15

12y - y² = 15

0 = y² - 12y + 15

    ↓     ↓         ↓

  a=1   b= -12   c=15

.\  y=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\.\quad =\dfrac{-(-12)\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}\\\\\\.\quad =\dfrac{12\pm \sqrt{144-120}}{2}\\\\\\.\quad =\dfrac{12\pm \sqrt{24}}{2}\\\\\\.\quad =\dfrac{12\pm 2\sqrt{6}}{2}\\\\\\.\quad =6\pm \sqrt{6}

Now, let's solve for x:

xy=15\\\\x(6\pm\sqrt6)=15\\\\x=\dfrac{15}{6\pm\sqrt6}\\\\\\x=\dfrac{15}{6\pm\sqrt6}\bigg(\dfrac{6\pm\sqrt6}{6\pm\sqrt6}\bigg)=\dfrac{6\pm \sqrt6}{2}

Lastly, find x² + y² :

y^2=(6\pm \sqrt6)^2\quad \rightarrow \quad y^2=36\pm 12\sqrt6 +6\quad \rightarrow \quad y^2=42\pm 12\sqrt6

x^2=\bigg(\dfrac{6\pm \sqrt6}{2}\bigg)^2\quad \rightarrow \quad x^2=\dfrac{42\pm 12\sqrt6}{4}\quad \rightarrow \quad x^2=\dfrac{21\pm 6\sqrt6}{2}

                                                                                 

x^2+y^2=\dfrac{21\pm 6\sqrt6}{2}+42\pm 12\sqrt6\\\\\\.\qquad \quad = \dfrac{21\pm 6\sqrt6}{2}+\dfrac{84\pm 24\sqrt6}{2}\\\\\\. \qquad \quad = \dfrac{105\pm 18\sqrt6}{2}

5 0
3 years ago
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Alex

Given that, a bike wheel is 26 inches in diameter.

We need to convert bike wheel's diameter in millimeters .

Since, 1 inch = 25.4 millimeters.

So, to convert 26 into mm we need to multiply 26 each sides of this identity to convert this into mm. Hence,

1*26 inch = 25.4 * 26 mm.

So, 26 inches = 660.4 mm.

So, the bike wheel's diameter is 660.4 millimeters.

Hope this helps you!

6 0
3 years ago
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Answer:

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3 years ago
Luis earns a base salary of \$150.00$150.00 every week with an additional 14\%14% commission on everything he sells. Luis sold \
tester [92]

Answer: Luis earned $997.00 for last week.

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Just figure the difference ($847)

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4 0
3 years ago
The expression 1.08 + 1.02b predicts the end- of the year value if a financial portfolio where S is the value of the stocks and
iragen [17]

Answer:

We have

Stock = $200

Bonds = $100

Substitute these values into 1.08s+1.02b, where 's' is stock and 'b' is bond

.() + .() =

Predicted end of year value is $318

4 0
2 years ago
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