Question

How do we determine the number of each type of ticket sold?

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

Let the number of advance tickets sold be p and

Let the number of same-day tickets sold be q, such that:

`\begin{gathered} 20\text{ p + 40 q = 1400 -- equation 1} \\ p\text{ + q = 45 ----- equation 2} \end{gathered}`
`equation\text{ 2 x 20 = 20 p + 20 q = 900 -- equation 3}`
`\begin{gathered} equation\text{ 1 minus equation 3, we have that:} \\ 40\text{ q - 20 q = 1400 - 900} \\ 20\text{ q = 500} \\ Divide\text{ both sides by 20, we have that:} \\ q\text{ =}(500)/(20)=\text{ 25} \\ q\text{ = 25} \\ since\text{ q = 25, put the value of q in equation 1:} \\ p\text{ + q = 45} \\ p\text{ + 25 = 45} \\ p\text{ = 45 - 25} \\ p\text{ = 20} \\ \end{gathered}`

CONCLUSION:

The number of advance tickets sold = 20

The number of same-day tickets sold = 25