Middle School

A movie theater charges $8 for adults and $4 for seniors. On a particular day, when 353 people paid admission, the total receipts were $1,688.

Answer :

A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults?
. How many who paid were seniors?

Answer:

There were 69 adults and 284 seniors

Solution:

Let "a" be the number of adults

Let "s" be the number of seniors

Cost of 1 adult = $ 8

Cost of 1 senior = $ 4

On a particular day when 353 people paid an admission

Therefore,

number of adults + number of seniors = 353

a + s = 353

a = 353 - s ---------- eqn 1

The total receipts were 1688 dollars

Therefore, we frame a equation as:

number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688

[tex]a \times 8 + s \times 4 = 1688[/tex]

8a + 4s = 1688 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

8(353 - s) + 4s = 1688

2824 -8s + 4s = 1688

4s = 2824 - 1688

4s = 1136

s = 284

Substitute s = 284 in eqn 1

a = 353 - 284

a = 69

Thus there were 69 adults and 284 seniors in movie theater

there were 55 adults and 284 seniors who paid admission.

Let's denote:

- ( A ) as the number of adults.

- ( S ) as the number of seniors.

Given:

- The price for adults is $9.

- The price for seniors is $5.

- The total number of people who paid admission is 339.

- The total receipts were $1915.

We can set up a system of equations based on the given information:

1. The total number of people who paid admission:

[tex]\[ A + S = 339 \][/tex]

2. The total receipts:

[tex]\[ 9A + 5S = 1915 \][/tex]

Now, we can solve this system of equations.

Let's solve equation 1 for one of the variables (let's solve for ( A )):

[tex]\[ A = 339 - S \][/tex]

Now, substitute this expression for( A ) into equation 2:

[tex]\[ 9(339 - S) + 5S = 1915 \][/tex]

Now, solve for \( S \):

[tex]\[ 3051 - 9S + 5S = 1915 \][/tex]

[tex]\[ -4S = 1915 - 3051 \][/tex]

[tex]\[ -4S = -1136 \][/tex]

[tex]\[ S = \frac{-1136}{-4} \][/tex]

[tex]\[ S = 284 \][/tex]

Now, we can find ( A ) using the value of ( S ) we found:

[tex]\[ A = 339 - 284 \][/tex]

[tex]\[ A = 55 \][/tex]

So, there were 55 adults and 284 seniors who paid admission.

complete question given below:

A movie theater charges 9$ for adults and 5 for seniors.on a particular day when 339 people paid an admission,the total receipts were 1915$ how many who paid were adults and how many who paid were seniors