Question

Brianna is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $3.75. Brianna spent $18.75 altogether at the carnival and the number of games she played is twice the number of rides she went on. Graphically solve a system of equations in order to determine the number of games Brianna played, x,x, and the number of rides Brianna went on, yy.

Answer 1

6 games=$7.5 3 rides=$11.25

1.25*6=7.5

3.75*3=11.25

7.5+11.25=18.75

Answer 2

6 games and 3 rides

Explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

x= 2y -----(1)

Total costs= cost of games +cost of rides

`18.75= 1.25x +3.75y`

Multiply the whole equation by 4 to remove the decimals:

`75= 5x +15y`

Simplify by dividing the whole equation by 5:

`15 = x + 3y`

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

x= 2y -----(1)

`\begin{tabular}c</p><p></p><p></p><p></p><p> \cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\</p><p></p><p> \cline{1-4}y & 1 &2&3\\</p><p></p><p></p><p> \cline{1-4}</p><p></p><p>\end{tabular}`

x +3y= 15 -----(2)

x= -3y +15

`\begin{tabular}c</p><p></p><p></p><p></p><p> \cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\</p><p></p><p> \cline{1-4}y & 1 &2&3\\</p><p></p><p></p><p> \cline{1-4}</p><p></p><p>\end{tabular}`

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.