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.

6 games and 3 rides

Step-by-step 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

Multiply the whole equation by 4 to remove the decimals:

Simplify by dividing the whole equation by 5:

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)

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

x= -3y +15

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.

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step-by-step explanation: