at the movie theatre, child admission is $6.10 and adult admission is $9.40. on sunday, 160 tickets were…

at the movie theatre, child admission is $6.10 and adult admission is $9.40. on sunday, 160 tickets were sold for a total sales of $1200.40. how many child tickets were sold that day?\nnumber of child tickets:

Answer

Explanation:

Step1: Let variables

Let $x$ be the number of child - tickets and $y$ be the number of adult - tickets. We know two equations based on the given information: Equation 1 (based on the number of tickets): $x + y=160$, so $y = 160 - x$. Equation 2 (based on the total sales): $6.1x+9.4y = 1200.4$.

Step2: Substitute $y$ into the second equation

Substitute $y = 160 - x$ into $6.1x + 9.4y=1200.4$. We get $6.1x+9.4(160 - x)=1200.4$. Expand the equation: $6.1x+1504-9.4x = 1200.4$.

Step3: Combine like - terms

Combine the $x$ terms: $6.1x-9.4x=1200.4 - 1504$. $-3.3x=1200.4 - 1504=-303.6$.

Step4: Solve for $x$

Divide both sides of the equation $-3.3x=-303.6$ by $-3.3$. $x=\frac{-303.6}{-3.3}=92$.