QuestionIf 1585 plasma TVs are sold, how many flatscreen TVs were sold if the ratio is 3:5? Also, for 27,360 total seats sold, find general admission seats if the ratio is 4:5.

Studdy Solution

STEP 1

Assumptions1. For every3 flatscreen TV sets sold,5 plasma TV sets were sold. . A total of1585 plasma TV sets were sold.
3. For every5 reserved seats sold for a concert,4 general admission seats were sold.
4. The total number of seats sold was27,360.

STEP 2

First, we need to find the ratio of flatscreen TV sets to plasma TV sets. This is given as5.

STEP 3

We can set up a proportion to find the number of flatscreen TV sets sold. The proportion is $\frac{Flatscreen\, TV\, sets}{Plasma\, TV\, sets} = \frac{3}{5}$

STEP 4

We know that158 plasma TV sets were sold. We can substitute this into the proportion $\frac{Flatscreen\, TV\, sets}{158} = \frac{3}{}$

STEP 5

To find the number of flatscreen TV sets sold, we can cross-multiply and solve for the unknown $Flatscreen\, TV\, sets = \frac{3}{5} \times1585$

STEP 6

Calculate the number of flatscreen TV sets sold $Flatscreen\, TV\, sets = \frac{3}{5} \times1585 =951$

STEP 7

Next, we need to find the ratio of reserved seats to general admission seats. This is given as54.

STEP 8

We can set up a proportion to find the number of general admission seats sold. The proportion is $\frac{Reserved\, seats}{General\, admission\, seats} = \frac{5}{4}$

STEP 9

We know that the total number of seats sold was27,360. This is the sum of the reserved seats and the general admission seats. We can write this as $Reserved\, seats + General\, admission\, seats =27360$

STEP 10

We can substitute the proportion from Step8 into the equation from Step9 $\frac{5}{4} \times General\, admission\, seats + General\, admission\, seats =27360$

STEP 11

implify the equation by combining like terms $\frac{9}{4} \times General\, admission\, seats =27360$

STEP 12

To find the number of general admission seats sold, we can solve for the unknown $General\, admission\, seats = \frac{27360}{\frac{9}{4}}$

STEP 13

Calculate the number of general admission seats sold $General\, admission\, seats = \frac{27360}{\frac{9}{}} =12160$ So,951 flatscreen TV sets and12160 general admission seats were sold.

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QuestionIf 1585 plasma TVs are sold, how many flatscreen TVs were sold if the ratio is 3:5? Also, for 27,360 total seats sold, find general admission seats if the ratio is 4:5.

Studdy Solution

STEP 1

Assumptions1. For every3 flatscreen TV sets sold,5 plasma TV sets were sold. . A total of1585 plasma TV sets were sold.
3. For every5 reserved seats sold for a concert,4 general admission seats were sold.
4. The total number of seats sold was27,360.

STEP 2

First, we need to find the ratio of flatscreen TV sets to plasma TV sets. This is given as5.

STEP 3

We can set up a proportion to find the number of flatscreen TV sets sold. The proportion is $\frac{Flatscreen\, TV\, sets}{Plasma\, TV\, sets} = \frac{3}{5}$

STEP 4

We know that158 plasma TV sets were sold. We can substitute this into the proportion $\frac{Flatscreen\, TV\, sets}{158} = \frac{3}{}$

STEP 5

To find the number of flatscreen TV sets sold, we can cross-multiply and solve for the unknown $Flatscreen\, TV\, sets = \frac{3}{5} \times1585$

STEP 6

Calculate the number of flatscreen TV sets sold $Flatscreen\, TV\, sets = \frac{3}{5} \times1585 =951$

STEP 7

Next, we need to find the ratio of reserved seats to general admission seats. This is given as54.

STEP 8

We can set up a proportion to find the number of general admission seats sold. The proportion is $\frac{Reserved\, seats}{General\, admission\, seats} = \frac{5}{4}$

STEP 9

We know that the total number of seats sold was27,360. This is the sum of the reserved seats and the general admission seats. We can write this as $Reserved\, seats + General\, admission\, seats =27360$

STEP 10

We can substitute the proportion from Step8 into the equation from Step9 $\frac{5}{4} \times General\, admission\, seats + General\, admission\, seats =27360$

STEP 11

implify the equation by combining like terms $\frac{9}{4} \times General\, admission\, seats =27360$

STEP 12

To find the number of general admission seats sold, we can solve for the unknown $General\, admission\, seats = \frac{27360}{\frac{9}{4}}$

STEP 13

Calculate the number of general admission seats sold $General\, admission\, seats = \frac{27360}{\frac{9}{}} =12160$ So,951 flatscreen TV sets and12160 general admission seats were sold.

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QuestionIf 1585 plasma TVs are sold, how many flatscreen TVs were sold if the ratio is 3:5? Also, for 27,360 total seats sold, find general admission seats if the ratio is 4:5.

Studdy Solution

STEP 1

Assumptions1. For every3 flatscreen TV sets sold,5 plasma TV sets were sold. . A total of1585 plasma TV sets were sold.3. For every5 reserved seats sold for a concert,4 general admission seats were sold.4. The total number of seats sold was27,360.

STEP 2

First, we need to find the ratio of flatscreen TV sets to plasma TV sets. This is given as5.

STEP 3

We can set up a proportion to find the number of flatscreen TV sets sold. The proportion isFlatscreen TV setsPlasma TV sets=35\frac{Flatscreen\, TV\, sets}{Plasma\, TV\, sets} = \frac{3}{5}PlasmaTVsetsFlatscreenTVsets​=53​

STEP 4

We know that158 plasma TV sets were sold. We can substitute this into the proportionFlatscreen TV sets158=3\frac{Flatscreen\, TV\, sets}{158} = \frac{3}{}158FlatscreenTVsets​=3​

STEP 5

To find the number of flatscreen TV sets sold, we can cross-multiply and solve for the unknownFlatscreen TV sets=35×1585Flatscreen\, TV\, sets = \frac{3}{5} \times1585FlatscreenTVsets=53​×1585

STEP 6

Calculate the number of flatscreen TV sets soldFlatscreen TV sets=35×1585=951Flatscreen\, TV\, sets = \frac{3}{5} \times1585 =951FlatscreenTVsets=53​×1585=951

STEP 7

Next, we need to find the ratio of reserved seats to general admission seats. This is given as54.

STEP 8

We can set up a proportion to find the number of general admission seats sold. The proportion isReserved seatsGeneral admission seats=54\frac{Reserved\, seats}{General\, admission\, seats} = \frac{5}{4}GeneraladmissionseatsReservedseats​=45​

STEP 9

We know that the total number of seats sold was27,360. This is the sum of the reserved seats and the general admission seats. We can write this asReserved seats+General admission seats=27360Reserved\, seats + General\, admission\, seats =27360Reservedseats+Generaladmissionseats=27360

STEP 10

We can substitute the proportion from Step8 into the equation from Step954×General admission seats+General admission seats=27360\frac{5}{4} \times General\, admission\, seats + General\, admission\, seats =2736045​×Generaladmissionseats+Generaladmissionseats=27360

STEP 11

implify the equation by combining like terms94×General admission seats=27360\frac{9}{4} \times General\, admission\, seats =2736049​×Generaladmissionseats=27360

STEP 12

To find the number of general admission seats sold, we can solve for the unknownGeneral admission seats=2736094General\, admission\, seats = \frac{27360}{\frac{9}{4}}Generaladmissionseats=49​27360​

STEP 13

Calculate the number of general admission seats soldGeneral admission seats=273609=12160General\, admission\, seats = \frac{27360}{\frac{9}{}} =12160Generaladmissionseats=9​27360​=12160So,951 flatscreen TV sets and12160 general admission seats were sold.

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Assumptions1. For every3 flatscreen TV sets sold,5 plasma TV sets were sold. . A total of1585 plasma TV sets were sold.
3. For every5 reserved seats sold for a concert,4 general admission seats were sold.
4. The total number of seats sold was27,360.

We can set up a proportion to find the number of flatscreen TV sets sold. The proportion is $\frac{Flatscreen\, TV\, sets}{Plasma\, TV\, sets} = \frac{3}{5}$

We know that158 plasma TV sets were sold. We can substitute this into the proportion $\frac{Flatscreen\, TV\, sets}{158} = \frac{3}{}$

To find the number of flatscreen TV sets sold, we can cross-multiply and solve for the unknown $Flatscreen\, TV\, sets = \frac{3}{5} \times1585$

Calculate the number of flatscreen TV sets sold $Flatscreen\, TV\, sets = \frac{3}{5} \times1585 =951$

We can set up a proportion to find the number of general admission seats sold. The proportion is $\frac{Reserved\, seats}{General\, admission\, seats} = \frac{5}{4}$

We know that the total number of seats sold was27,360. This is the sum of the reserved seats and the general admission seats. We can write this as $Reserved\, seats + General\, admission\, seats =27360$

We can substitute the proportion from Step8 into the equation from Step9 $\frac{5}{4} \times General\, admission\, seats + General\, admission\, seats =27360$

implify the equation by combining like terms $\frac{9}{4} \times General\, admission\, seats =27360$

To find the number of general admission seats sold, we can solve for the unknown $General\, admission\, seats = \frac{27360}{\frac{9}{4}}$

Calculate the number of general admission seats sold $General\, admission\, seats = \frac{27360}{\frac{9}{}} =12160$ So,951 flatscreen TV sets and12160 general admission seats were sold.