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3 years ago

8

A small theater sold 72 tickets for a play. The ratio of adult tickets to child tickets was 4:1. The ratio of adult tickets to s

enior tickets was 4:3. How many of each type of ticket were sold?

1 answer:

Y_Kistochka [10]3 years ago

3 0

Answer:

Adult 36

Children 9

senior 27

Step-by-step explanation:

We have 3 types of tickets as seen from the question;

Adult, children and seniors tickets.

Now, looking at the question critically,

Since the ratio of adults to children and senior citizens stands at 4: a specific value, we can then conclude that the ratio of tickets sold is 4:1:3

where 1 and 3 represents the ratio for the children and seniors respectively

So let’s calculate the individual ratio now.

For the total, we have 4 + 1 + 3 = 8

Thus, for the adults, we have 4/8 * 72 = 36

For the children, we have 1/8 * 72 = 9

For the seniors, we have 3/8 * 72 = 27

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siniylev [52]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

$\frac{x}{2}-\frac{y}{5}=1$ ----> equation A

$y-\frac{x}{3}=8$ ----> equation B

Multiply equation A by 10 both sides to remove the fractions

$5x-2y=10$ ----> equation C

isolate the variable y in equation B

$y=\frac{x}{3}+8$ ----> equation D

we have the system of equations

$5x-2y=10$ ----> equation C

$y=\frac{x}{3}+8$ ----> equation D

Solve the system by substitution

substitute equation D in equation C

$5x-2(\frac{x}{3}+8)=10$

solve for x

$5x-\frac{2x}{3}-16=10$

Multiply by 3 both sides

$15x-2x-48=30$

$15x-2x=48+30$

Combine like terms

$13x=78$

$x=6$

<em>Find the value of y</em>

$y=\frac{x}{3}+8$

$y=\frac{6}{3}+8$

$y=10$

The solution is the ordered pair (6,10)

Part b) we have

$xy=21$ ---> equation A

$x+5y=22$ ----> equation B

isolate the variable x in the equation B

$x=22-5y$ ----> equation C

substitute equation C in equation A

$(22-5y)y=21$

solve for y

$22y-5y^2=21$

$5y^2-22y+21=0$

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

<em>Find the values of x</em>

For y=1.4

$x=22-5(1.4)=15$

For y=3

$x=22-5(3)=7$

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The solutions are the ordered pairs (7,3) and (15,1.4)

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4 years ago

Dependent and Independent variables? I am plotting points on a scatterplot and I'm not sure where to place my variables. The num

IrinaK [193]

Answer:

The number of confirmed cases is the independent variable.

The number of deaths is the dependent variable.

Why?

<u>The number of deaths is dependent on the fact that there are cases, so the number of deaths is a dependent variable.</u>

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3 years ago

Gordon, Henry and Sarah share £48 in a ratio 2:3:1. How much money does each person get?

Alinara [238K]

Answer:

Gordon gets 16£, Henry gets 24£ and Sarah gets 8£

Step-by-step explanation:

Let the ratio be 2x + 3x + 1x

Total amount = £48

So;

2x + 3x + x = 48

6x = 48

x = 48 / 6

x = 8

Now

2x = 16

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3 years ago

7. Evaluate 4P2<br><br> O<br><br> 22<br><br> O<br><br> 12<br><br> O<br><br> 14<br><br> 5

Reika [66]

Answer:

<h2>12</h2>

Step-by-step explanation:

To evaluate 4P2, we will use the permutation formula as shown;

nPr = $\frac{n!}{(n-r)!}$

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adoni [48]

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3 years ago