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
