Question

Write a systems of equations for each problem define variables used. Please show all work There were 166 paid admissions to a game. The price was $2.10 for adults and $ 0.75 each for children the amount taken in was $293.25 how many adults and how many children attended?Problem2 On a table are 20 coins, quarters and dimes. Their value is $3.05 how many of each kind of coin are there?

Answer 1

Let x be the number of adults that went to the game, and y be the number of children, since the number of total of people that went to the game is 166, then:

`x+y=166.`

Now, each adult ticket had a cost of $2.10, each child's ticket had a cost of $0.75, and the total amount taken in was $293.25. Therefore:

`2.10x+0.75y=293.25.`

Solving the first equation for x we get:

`x=166-y\text{.}`

Substituting the above equation in the second equation and solving for y we get:

`\begin{gathered} 2.10\cdot(166-y)+0.75y=293.25, \\ 348.6-2.10y+0.75y=293.25, \\ -1.35y=-55.35, \\ y=41. \end{gathered}`

Substituting y=41 in the third equation on the board we get:

`\begin{gathered} x=166-41, \\ x=125. \end{gathered}`

Answer:

The system of equations is:

`\begin{gathered} x+y=166, \\ 2.10x+0.75y=293.25. \end{gathered}`

Where x is the number of adults that went to the game and y is the number of children.

The number of adults that attended is 125 and the number of children is 41.