Interpret the graph to find the solution for the following scenario. How do you know this is a reasonable answer?
The players on a softball team held a car wash to raise money for new uniforms. They charged $5 per car and $8 per truck or SUV. If they earned a total of $575 by washing 100 vehicles, how many cars and how many trucks/SUVs did they wash? Let x represent the number of cars and y represent the number of trucks/SUVs.
To interpret the graph and find the solution for this scenario, we can set up a system of equations based on the information given.
Let's assume that the number of cars washed is represented by x, and the number of trucks/SUVs washed is represented by y.
According to the scenario, the players charged $5 per car and $8 per truck/SUV. Therefore, the total amount earned from cars would be 5x, and the total amount earned from trucks/SUVs would be 8y.
Additionally, the total amount earned from washing 100 vehicles is $575. Therefore, we can write the equation:
5x + 8y = 575
We need to determine the values of x and y that satisfy this equation.
To find a reasonable solution, we can look at the graph of this equation. The graph may consist of a straight line that represents all possible combinations of x and y that satisfy the equation.
By examining the graph, we can determine the point(s) at which the line intersects the axes, which represent the possible number of cars and the possible number of trucks/SUVs washed.
The coordinates of the intersection point(s) on the graph represent the solution(s) to the given scenario.
To verify if this solution is reasonable, we can substitute the values of x and y into the original equation and check if it satisfies the condition mentioned in the scenario.
For example, if the graph shows that x = 50 and y = 25, we can substitute these values into the equation:
5x + 8y = 575
5(50) + 8(25) = 575
250 + 200 = 575
450 = 575
This equation is false, meaning that the solution (x = 50, y = 25) is not reasonable for this scenario as it does not satisfy the given condition.
We need to find the point(s) on the graph where the equation is true, indicating the correct solution(s) in terms of the number of cars and trucks/SUVs washed.