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dusya [7]
2 years ago
9

A rectangular school banner has a length of 36 inches and a width of 52 inches. A sign is made that is similar to the school ban

ner and has a length of 22 inches. What is the ratio of the area of the school banner to the area of the sign
Mathematics
1 answer:
zalisa [80]2 years ago
8 0

Answer:

<u>4212 : 1573</u> is the ratio.

Step-by-step explanation:

Given:

Length of rectangular school banner is 36 inches and width is 52 inches.

And, the sign made is similar to banner.

The sign's length is 22 inches.

Now, we have to find the ratio of the area of the banner to the area of the sign.

So, we have dimensions of rectangular school banner:

Length = 36 inches.

Width = 52 inches.

But, we have only length of sign:

Length = 22 inches.

Now, we have to find the width of sign by using cross multiplication method:

Let the width of sign be x.

<em>As, sign is similar to banner.</em>

So, if 36 inches is equivalent to 52 inches.

Then, 22 inches is equivalent to x.

\frac{36}{52} =\frac{22}{x}

<em>By cross multiplying we get:</em>

<em />36x=1144<em />

<em>Dividing both sides by 36 we get:</em>

x=31\frac{7}{9} .

<em>Hence, the width of sign is </em>31\frac{7}{9}<em> inches.</em>

Now, we find the area of banner and the area of sign by putting formula:

Area of banner = length × width.

Area\ of\ banner=36\times 52

Area\ of\ banner=1872\ square\ inches.

Now, area of sign:

Area\ of\ sign=length\times width\\\\Area\ of\ sign=22\times 31\frac{7}{9} \\\\Area\ of\ sign=22\times \frac{286}{9} \\\\Area\ of\ sign=\frac{6292}{9} \ square\ inches.

Now, to get the ratio of the area of the school banner to the area of the sign:

1872:\frac{6292}{9}

=\frac{1872}{\frac{6292}{9} } \\\\=\frac{16848}{6292}

<em>On simplifying we get:</em>

=\frac{4212}{1573}

=4212:1573.

Therefore, the ratio of the area of the school banner to the area of the sign is 4212:1573.

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A movie theater has a seating capacity of 197. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults.
yarga [219]

Answer: 74 children attended

86 students attended

37 adults attended

Step-by-step explanation:

Let x represent the number of children that attended.

Let y represent the number of students that attended.

Let z represent the number of adults that attended.

The movie theater has a seating capacity of 197. It means that

x + y + z = 197- - - - - - - - - - - - -1

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. If the total ticket sales was $ 1416, It means that

5x + 7y + 12z = 1416- - - - - - - - - - 2

There are half as many adults as there are children. It means that

It means that

z = x/2

x = 2z

Substituting x = 2z into equation 1 and equation 2, it becomes

2z + y + z = 197

y + 3z = 197- - - - - - - - - - - - -3

5 × 2z + 7y + 12z = 1416

10z + 7y + 12z = 1416

7y + 22z = 1416- - - - - - - - - - - 4

Multiplying equation 3 by 7 and equation 4 by 1, it becomes

7y + 21z = 1379

7y + 22z = 1416

Subtracting, it becomes

- z = - 37

z = 37

x = 2z = 2 × 37

x = 74

Substituting x = 74 and z = 37 into equation 1, it becomes

74 + y + 37 = 197

y = 197 - 74 - 37

y = 86

5 0
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