Question

Rendering math...Five adults and four children go to the museum. They pay a total of $19 for admission. Theadult admission fee is three times the fee for a child. If an adult ticket costs x dollars and a ticket for a childcosts y dollars, which of the following statements are correct? Select all that apply.One of the equations to be used in solving the problem is x=3y.After a possible substitution, 53y+4y=19 can be obtained.One of the equations to be used in solving the problem is y=3x.After a possible substitution, 53x+4x=19can be obtainedThe adult fee is 3 dollars.The ticket for a child costs 2 dollars.5One of the equations to be used in solving the problem is x=3y.After a possible substitution, 53y+4y=19 can be obtained.One of the equations to be used in solving the problem is y=3x.After a possible substitution, 53x+4x=19can be obtained.The adult fee is 3 dollars.English (US)ere to searchE1515 +G

Answer 1

Let be "x" the cost in dollars of an adult ticket and "y" the cost in dollars of a child ticket.

You know that a 5 adults and 4 children went to the museum and the total cost was $19. Therefore, you can write the following equation:

`5x+4y=19`

The word "Three times" indicates a multiplication by 3. Therefore, "The

adult admission fee is three times the fee for a child" can be written as:

`x=3y`

In order to find the values of "x" and "y", substitute the second equation into the first one and solve for "y":

`\begin{gathered} 5(3y)+4y=19 \\ 15y+4y=19 \\ 19y=19 \\ y=1 \end{gathered}`

To find "x", substitute the value of "y" into the second equation. Then:

`\begin{gathered} x=3(1) \\ x=3 \end{gathered}`

Therefore, you can identify that the correct options are:

- One of the equations to be used in solving the problem is :

`x=3y`

- The adult fee is 3 dollars.