Solved on Jan 30, 2024

Find the number of blue seats in a theater with 88 seats split into 4 identical sections, each with 14 red seats.

STEP 1

Assumptions
1. The total number of seats in the theater is 88.
2. The theater is divided into 4 identical sections.
3. Each section has 14 red seats.
4. The rest of the seats in each section are blue.

STEP 2

First, we need to calculate the total number of red seats in the theater by multiplying the number of red seats in one section by the number of sections.
$Total\, red\, seats = Number\, of\, red\, seats\, per\, section \times Number\, of\, sections$

STEP 3

Now, plug in the given values for the number of red seats per section and the number of sections to calculate the total number of red seats.
$Total\, red\, seats = 14 \times 4$

STEP 4

Calculate the total number of red seats.
$Total\, red\, seats = 14 \times 4 = 56$

STEP 5

To find the total number of blue seats in the theater, we subtract the total number of red seats from the total number of seats in the theater.
$Total\, blue\, seats = Total\, number\, of\, seats - Total\, red\, seats$

STEP 6

Plug in the values for the total number of seats and the total number of red seats to calculate the total number of blue seats.
$Total\, blue\, seats = 88 - 56$

STEP 7

Calculate the total number of blue seats.
$Total\, blue\, seats = 88 - 56 = 32$

STEP 8

Now, to find the number of blue seats per section, divide the total number of blue seats by the number of sections.
$Blue\, seats\, per\, section = Total\, blue\, seats / Number\, of\, sections$

STEP 9

Plug in the values for the total number of blue seats and the number of sections to calculate the number of blue seats per section.
$Blue\, seats\, per\, section = 32 / 4$

STEP 10

Calculate the number of blue seats per section.
$Blue\, seats\, per\, section = 32 / 4 = 8$

STEP 11

Now we can represent the situation with a tape diagram or hanger. Since the problem does not specify which to use, we will describe how to draw a tape diagram.
- Draw a rectangle and divide it into 4 equal parts to represent the 4 sections. - In each section, draw 14 small squares and color them red to represent the red seats. - Then draw 8 small squares in a different color (blue) to represent the blue seats.

STEP 12

To write an equation that represents the situation, let's denote the total number of seats in each section as $S$ , the number of red seats as $R$ , and the number of blue seats as $B$ . Since each section is identical, we can write:
$S = R + B$

STEP 13

Now, plug in the values for $R$ and $B$ to represent the situation for one section.
$S = 14 + 8$

STEP 14

Calculate the total number of seats in one section.
$S = 14 + 8 = 22$

STEP 15

Finally, we can write the equation that represents the entire theater by multiplying the number of seats in one section by the number of sections.
$Total\, number\, of\, seats = S \times Number\, of\, sections$

STEP 16

Plug in the values for $S$ and the number of sections to represent the situation for the entire theater.
$Total\, number\, of\, seats = 22 \times 4$

STEP 17

Calculate the total number of seats in the theater.
$Total\, number\, of\, seats = 22 \times 4 = 88$
This confirms our initial total and completes the equation representing the situation.

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Find the number of blue seats in a theater with 88 seats split into 4 identical sections, each with 14 red seats.

STEP 1

Assumptions
1. The total number of seats in the theater is 88.
2. The theater is divided into 4 identical sections.
3. Each section has 14 red seats.
4. The rest of the seats in each section are blue.

STEP 2

First, we need to calculate the total number of red seats in the theater by multiplying the number of red seats in one section by the number of sections.
$Total\, red\, seats = Number\, of\, red\, seats\, per\, section \times Number\, of\, sections$

STEP 3

Now, plug in the given values for the number of red seats per section and the number of sections to calculate the total number of red seats.
$Total\, red\, seats = 14 \times 4$

STEP 4

Calculate the total number of red seats.
$Total\, red\, seats = 14 \times 4 = 56$

STEP 5

To find the total number of blue seats in the theater, we subtract the total number of red seats from the total number of seats in the theater.
$Total\, blue\, seats = Total\, number\, of\, seats - Total\, red\, seats$

STEP 6

Plug in the values for the total number of seats and the total number of red seats to calculate the total number of blue seats.
$Total\, blue\, seats = 88 - 56$

STEP 7

Calculate the total number of blue seats.
$Total\, blue\, seats = 88 - 56 = 32$

STEP 8

Now, to find the number of blue seats per section, divide the total number of blue seats by the number of sections.
$Blue\, seats\, per\, section = Total\, blue\, seats / Number\, of\, sections$

STEP 9

Plug in the values for the total number of blue seats and the number of sections to calculate the number of blue seats per section.
$Blue\, seats\, per\, section = 32 / 4$

STEP 10

Calculate the number of blue seats per section.
$Blue\, seats\, per\, section = 32 / 4 = 8$

STEP 11

STEP 12

To write an equation that represents the situation, let's denote the total number of seats in each section as $S$ , the number of red seats as $R$ , and the number of blue seats as $B$ . Since each section is identical, we can write:
$S = R + B$

STEP 13

Now, plug in the values for $R$ and $B$ to represent the situation for one section.
$S = 14 + 8$

STEP 14

Calculate the total number of seats in one section.
$S = 14 + 8 = 22$

STEP 15

Finally, we can write the equation that represents the entire theater by multiplying the number of seats in one section by the number of sections.
$Total\, number\, of\, seats = S \times Number\, of\, sections$

STEP 16

Plug in the values for $S$ and the number of sections to represent the situation for the entire theater.
$Total\, number\, of\, seats = 22 \times 4$

STEP 17

Calculate the total number of seats in the theater.
$Total\, number\, of\, seats = 22 \times 4 = 88$
This confirms our initial total and completes the equation representing the situation.

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Find the number of blue seats in a theater with 88 seats split into 4 identical sections, each with 14 red seats.

STEP 1

Assumptions1. The total number of seats in the theater is 88.2. The theater is divided into 4 identical sections.3. Each section has 14 red seats.4. The rest of the seats in each section are blue.

STEP 2

STEP 3

Now, plug in the given values for the number of red seats per section and the number of sections to calculate the total number of red seats.Total red seats=14×4Total\, red\, seats = 14 \times 4Totalredseats=14×4

STEP 4

Calculate the total number of red seats.Total red seats=14×4=56Total\, red\, seats = 14 \times 4 = 56Totalredseats=14×4=56

STEP 5

STEP 6

Plug in the values for the total number of seats and the total number of red seats to calculate the total number of blue seats.Total blue seats=88−56Total\, blue\, seats = 88 - 56Totalblueseats=88−56

STEP 7

Calculate the total number of blue seats.Total blue seats=88−56=32Total\, blue\, seats = 88 - 56 = 32Totalblueseats=88−56=32

STEP 8

STEP 9

Plug in the values for the total number of blue seats and the number of sections to calculate the number of blue seats per section.Blue seats per section=32/4Blue\, seats\, per\, section = 32 / 4Blueseatspersection=32/4

STEP 10

Calculate the number of blue seats per section.Blue seats per section=32/4=8Blue\, seats\, per\, section = 32 / 4 = 8Blueseatspersection=32/4=8

STEP 11

STEP 12

To write an equation that represents the situation, let's denote the total number of seats in each section as SSS, the number of red seats as RRR, and the number of blue seats as BBB. Since each section is identical, we can write:S=R+BS = R + BS=R+B

STEP 13

Now, plug in the values for RRR and BBB to represent the situation for one section.S=14+8S = 14 + 8S=14+8

STEP 14

Calculate the total number of seats in one section.S=14+8=22S = 14 + 8 = 22S=14+8=22

STEP 15

Finally, we can write the equation that represents the entire theater by multiplying the number of seats in one section by the number of sections.Total number of seats=S×Number of sectionsTotal\, number\, of\, seats = S \times Number\, of\, sectionsTotalnumberofseats=S×Numberofsections

STEP 16

Plug in the values for SSS and the number of sections to represent the situation for the entire theater.Total number of seats=22×4Total\, number\, of\, seats = 22 \times 4Totalnumberofseats=22×4

STEP 17

Calculate the total number of seats in the theater.Total number of seats=22×4=88Total\, number\, of\, seats = 22 \times 4 = 88Totalnumberofseats=22×4=88This confirms our initial total and completes the equation representing the situation.

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Assumptions
1. The total number of seats in the theater is 88.
2. The theater is divided into 4 identical sections.
3. Each section has 14 red seats.
4. The rest of the seats in each section are blue.

Now, plug in the given values for the number of red seats per section and the number of sections to calculate the total number of red seats.
$Total\, red\, seats = 14 \times 4$

Calculate the total number of red seats.
$Total\, red\, seats = 14 \times 4 = 56$

Plug in the values for the total number of seats and the total number of red seats to calculate the total number of blue seats.
$Total\, blue\, seats = 88 - 56$

Calculate the total number of blue seats.
$Total\, blue\, seats = 88 - 56 = 32$

Plug in the values for the total number of blue seats and the number of sections to calculate the number of blue seats per section.
$Blue\, seats\, per\, section = 32 / 4$

Calculate the number of blue seats per section.
$Blue\, seats\, per\, section = 32 / 4 = 8$

To write an equation that represents the situation, let's denote the total number of seats in each section as $S$ , the number of red seats as $R$ , and the number of blue seats as $B$ . Since each section is identical, we can write:
$S = R + B$

Now, plug in the values for $R$ and $B$ to represent the situation for one section.
$S = 14 + 8$

Calculate the total number of seats in one section.
$S = 14 + 8 = 22$

Finally, we can write the equation that represents the entire theater by multiplying the number of seats in one section by the number of sections.
$Total\, number\, of\, seats = S \times Number\, of\, sections$

Plug in the values for $S$ and the number of sections to represent the situation for the entire theater.
$Total\, number\, of\, seats = 22 \times 4$

Calculate the total number of seats in the theater.
$Total\, number\, of\, seats = 22 \times 4 = 88$
This confirms our initial total and completes the equation representing the situation.