20 points
1 answer:
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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
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.
Answer:
<h3>There is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.</h3>Step-by-step explanation:
Given the equation y = 750x which represents the number of dollars y Olivia earns in x weeks, from the equation, it can be inferred that the number of dollars olivia earns is DIRECTLY PROPORTIONAL to the number of weeks. This relationship is therefore a direct variation.
In direct variation, increase in a variable will lead to corresponding increase in the other variable and vice versa by a factor known as the constant of variation.
For example if y is directly proportional to x, it is written mathematically as shown;
where k is the constant of proportionality.
comparing the general expression above with the equation in question,
y = 750x
k = 750
Therefore we can conclude that there is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.