Solved on Sep 25, 2023

Find the number of general admission and reserved seating tickets sold, given the total receipts of $\$ 7031.00$ for 1358 paid admissions with $\$ 4.50$ for general and $\$ 7.00$ for reserved seats.

STEP 1

Assumptions1. The cost of a general admission ticket is $4.50. The cost of a reserved seat ticket is$ 7.003. The total receipts from the game were $7031.004. The total number of tickets sold (both general admission and reserved seats) was13585. We are looking for the number of each type of ticket sold

STEP 2

Let's denote the number of general admission tickets sold as $x$ and the number of reserved seating tickets sold as $y$ .

STEP 3

We can write down two equations based on the problem. The first equation is based on the total number of tickets sold $x + y =1358$

STEP 4

The second equation is based on the total receipts from the game $4.50x +7.00y =7031.00$

STEP 5

We can solve this system of equations using substitution or elimination method. Let's use the substitution method. First, let's solve the first equation for $x$ $x =1358 - y$

STEP 6

Now, substitute $x$ in the second equation $4.50(1358 - y) +.00y =7031.00$

STEP 7

implify the equation $6111 -4.50y +7.00y =7031.00$

STEP 8

Combine like terms $2.50y =920$

STEP 9

olve for $y$ $y = \frac{920}{2.5}$

STEP 10

Calculate the value of $y$ $y = \frac{920}{2.5} =368$

STEP 11

Now that we have the value of $y$ , we can find the value of $x$ by substituting $y$ into the first equation $x =1358 -368$

STEP 12

Calculate the value of $x$ $x =1358 -368 =990$ So,990 general admission tickets and368 reserved seating tickets were sold.

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Find the number of general admission and reserved seating tickets sold, given the total receipts of $\$ 7031.00$ for 1358 paid admissions with $\$ 4.50$ for general and $\$ 7.00$ for reserved seats.

STEP 1

STEP 2

Let's denote the number of general admission tickets sold as $x$ and the number of reserved seating tickets sold as $y$ .

STEP 3

We can write down two equations based on the problem. The first equation is based on the total number of tickets sold $x + y =1358$

STEP 4

The second equation is based on the total receipts from the game $4.50x +7.00y =7031.00$

STEP 5

We can solve this system of equations using substitution or elimination method. Let's use the substitution method. First, let's solve the first equation for $x$ $x =1358 - y$

STEP 6

Now, substitute $x$ in the second equation $4.50(1358 - y) +.00y =7031.00$

STEP 7

implify the equation $6111 -4.50y +7.00y =7031.00$

STEP 8

Combine like terms $2.50y =920$

STEP 9

olve for $y$ $y = \frac{920}{2.5}$

STEP 10

Calculate the value of $y$ $y = \frac{920}{2.5} =368$

STEP 11

Now that we have the value of $y$ , we can find the value of $x$ by substituting $y$ into the first equation $x =1358 -368$

STEP 12

Calculate the value of $x$ $x =1358 -368 =990$ So,990 general admission tickets and368 reserved seating tickets were sold.

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Find the number of general admission and reserved seating tickets sold, given the total receipts of $7031.00\$ 7031.00$7031.00 for 1358 paid admissions with $4.50\$ 4.50$4.50 for general and $7.00\$ 7.00$7.00 for reserved seats.

STEP 1

STEP 2

Let's denote the number of general admission tickets sold as xxx and the number of reserved seating tickets sold as yyy.

STEP 3

We can write down two equations based on the problem. The first equation is based on the total number of tickets soldx+y=1358x + y =1358x+y=1358

STEP 4

The second equation is based on the total receipts from the game4.50x+7.00y=7031.004.50x +7.00y =7031.004.50x+7.00y=7031.00

STEP 5

We can solve this system of equations using substitution or elimination method. Let's use the substitution method. First, let's solve the first equation for xxxx=1358−yx =1358 - yx=1358−y

STEP 6

Now, substitute xxx in the second equation4.50(1358−y)+.00y=7031.004.50(1358 - y) +.00y =7031.004.50(1358−y)+.00y=7031.00

STEP 7

implify the equation6111−4.50y+7.00y=7031.006111 -4.50y +7.00y =7031.006111−4.50y+7.00y=7031.00

STEP 8

Combine like terms2.50y=9202.50y =9202.50y=920

STEP 9

olve for yyyy=9202.5y = \frac{920}{2.5}y=2.5920​

STEP 10

Calculate the value of yyyy=9202.5=368y = \frac{920}{2.5} =368y=2.5920​=368

STEP 11

Now that we have the value of yyy, we can find the value of xxx by substituting yyy into the first equationx=1358−368x =1358 -368x=1358−368

STEP 12

Calculate the value of xxxx=1358−368=990x =1358 -368 =990x=1358−368=990So,990 general admission tickets and368 reserved seating tickets were sold.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the number of general admission and reserved seating tickets sold, given the total receipts of $\$ 7031.00$ for 1358 paid admissions with $\$ 4.50$ for general and $\$ 7.00$ for reserved seats.

Let's denote the number of general admission tickets sold as $x$ and the number of reserved seating tickets sold as $y$ .

We can write down two equations based on the problem. The first equation is based on the total number of tickets sold $x + y =1358$

The second equation is based on the total receipts from the game $4.50x +7.00y =7031.00$

We can solve this system of equations using substitution or elimination method. Let's use the substitution method. First, let's solve the first equation for $x$ $x =1358 - y$

Now, substitute $x$ in the second equation $4.50(1358 - y) +.00y =7031.00$

implify the equation $6111 -4.50y +7.00y =7031.00$

Combine like terms $2.50y =920$

olve for $y$ $y = \frac{920}{2.5}$

Calculate the value of $y$ $y = \frac{920}{2.5} =368$

Now that we have the value of $y$ , we can find the value of $x$ by substituting $y$ into the first equation $x =1358 -368$

Calculate the value of $x$ $x =1358 -368 =990$ So,990 general admission tickets and368 reserved seating tickets were sold.