Answer:
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
[tex]18.75= 1.25x +3.75y[/tex]
Multiply the whole equation by 4 to remove the decimals:
[tex]75= 5x +15y[/tex]
Simplify by dividing the whole equation by 5:
[tex]15 = x + 3y[/tex]
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)
[tex]\begin{tabular}{|c|c|c|c|}
\cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\
\cline{1-4}y & 1 &2&3\\
\cline{1-4}
\end{tabular}[/tex]
x +3y= 15 -----(2)
x= -3y +15
[tex]\begin{tabular}{|c|c|c|c|}
\cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\
\cline{1-4}y & 1 &2&3\\
\cline{1-4}
\end{tabular}[/tex]
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.
Answer:
6 games=$7.5 3 rides=$11.25
1.25*6=7.5
3.75*3=11.25
7.5+11.25=18.75
