Question

I need help with my homework please it’s 3 parts to this question I will post the rest into the answer tab

Answer 1

Since there are a adults and c children

Since there are 187 tickets sold

Then the number of adults and children is 187

Add a and c, then equate the sum by 187

`a+c=187\rightarrow(1)`

Since the price of each adult's ticket is $25

Since the price of each child ticket is $13

Since the total revenue is $3223

Then multiply a by 25, c by 13, then add the products and equate the sum by $3223

`25a+13c=3223\rightarrow(2)`

Now, we have a system of equations to solve it

Multiply equation (1) by -13 to make c equal in values and opposite in signs to eliminate it

`\begin{gathered} -13(a)+-13(c)=-13(187) \\ -13a-13c=-2431\rightarrow(3) \end{gathered}`

Add equations (2) and (3)

`\begin{gathered} (25a-13a)+(13c-13c)=(3223-2431) \\ 12a=792 \end{gathered}`

Divide both sides by 12

`\begin{gathered} (12a)/(12)=(792)/(12) \\ a=66 \end{gathered}`

Substitute a by 66 in equation (1) to find c

`66+c=187`

Subtract 66 from both sides

`\begin{gathered} 66-66+c=187-66 \\ c=121 \end{gathered}`

The answers are:

a) The system of equations is

`\begin{gathered} a+c=187 \\ 25a+13c=3223 \end{gathered}`

b) There were 66 adult tickets sold

c) There were 121 children's tickets sold