Answer :
To solve the problem of determining the cost for a family consisting of 2 senior citizens and 3 children to attend the choral performance, we should find the price of each senior citizen ticket and each child ticket using the information provided:
1. Setup the Equations from Sales Data:
- On the first day, the school sold 3 senior citizen tickets and 1 child ticket for a total of [tex]$38.
- On the second day, the school sold 3 senior citizen tickets and 2 child tickets for a total of $[/tex]52.
Let’s denote:
- [tex]\( s \)[/tex] as the price of a senior citizen ticket.
- [tex]\( c \)[/tex] as the price of a child ticket.
We can set up the following equations based on the sales data:
[tex]\[
3s + 1c = 38 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
3s + 2c = 52 \quad \text{(Equation 2)}
\][/tex]
2. Solve the Equations:
From Equation 1:
[tex]\[
3s + c = 38
\][/tex]
From Equation 2:
[tex]\[
3s + 2c = 52
\][/tex]
To eliminate [tex]\( s \)[/tex], subtract Equation 1 from Equation 2:
[tex]\[
(3s + 2c) - (3s + c) = 52 - 38
\][/tex]
[tex]\[
c = 14
\][/tex]
Now, substitute [tex]\( c = 14 \)[/tex] back into Equation 1 to find [tex]\( s \)[/tex]:
[tex]\[
3s + 14 = 38
\][/tex]
[tex]\[
3s = 38 - 14
\][/tex]
[tex]\[
3s = 24
\][/tex]
[tex]\[
s = 8
\][/tex]
So, the price of a senior citizen ticket [tex]\( s \)[/tex] is [tex]$8, and the price of a child ticket \( c \) is $[/tex]14.
3. Calculate the Total Cost for the Family:
The family consists of 2 senior citizens and 3 children. Therefore, the total cost for the family is calculated as follows:
[tex]\[
\text{Total cost} = 2s + 3c
\][/tex]
[tex]\[
\text{Total cost} = 2(8) + 3(14)
\][/tex]
[tex]\[
\text{Total cost} = 16 + 42
\][/tex]
[tex]\[
\text{Total cost} = 58
\][/tex]
Therefore, it would cost the family a total of $58 to attend the choral performance.
1. Setup the Equations from Sales Data:
- On the first day, the school sold 3 senior citizen tickets and 1 child ticket for a total of [tex]$38.
- On the second day, the school sold 3 senior citizen tickets and 2 child tickets for a total of $[/tex]52.
Let’s denote:
- [tex]\( s \)[/tex] as the price of a senior citizen ticket.
- [tex]\( c \)[/tex] as the price of a child ticket.
We can set up the following equations based on the sales data:
[tex]\[
3s + 1c = 38 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
3s + 2c = 52 \quad \text{(Equation 2)}
\][/tex]
2. Solve the Equations:
From Equation 1:
[tex]\[
3s + c = 38
\][/tex]
From Equation 2:
[tex]\[
3s + 2c = 52
\][/tex]
To eliminate [tex]\( s \)[/tex], subtract Equation 1 from Equation 2:
[tex]\[
(3s + 2c) - (3s + c) = 52 - 38
\][/tex]
[tex]\[
c = 14
\][/tex]
Now, substitute [tex]\( c = 14 \)[/tex] back into Equation 1 to find [tex]\( s \)[/tex]:
[tex]\[
3s + 14 = 38
\][/tex]
[tex]\[
3s = 38 - 14
\][/tex]
[tex]\[
3s = 24
\][/tex]
[tex]\[
s = 8
\][/tex]
So, the price of a senior citizen ticket [tex]\( s \)[/tex] is [tex]$8, and the price of a child ticket \( c \) is $[/tex]14.
3. Calculate the Total Cost for the Family:
The family consists of 2 senior citizens and 3 children. Therefore, the total cost for the family is calculated as follows:
[tex]\[
\text{Total cost} = 2s + 3c
\][/tex]
[tex]\[
\text{Total cost} = 2(8) + 3(14)
\][/tex]
[tex]\[
\text{Total cost} = 16 + 42
\][/tex]
[tex]\[
\text{Total cost} = 58
\][/tex]
Therefore, it would cost the family a total of $58 to attend the choral performance.
