Answer:
x = 20, that is, after washing 20 cars.
Step-by-step explanation:
To write the equation that model this problem we have to use slope-intercept formula: [tex]y=mx+b[/tex].
The slope can be found using its definition, and two points from the table, could be [tex](0;30)[/tex] and [tex](12;12)[/tex]:
[tex]m=\frac{12-30}{12-0}=-\frac{-18}{12}=-\frac{6}{4}=-\frac{3}{2}[/tex]
From the table, we observe the intercept point [tex](0;30)[/tex], which is the interception with y-axis, this is the meaning of [tex]b[/tex]. So, replacing all values in the slope-intercept formula, we have:
[tex]y=-\frac{3}{2}x+30[/tex]
The meaning of the negative slope means that the functions is decreasing, that is, the amount of money decreases, while the number of car washed increase, that is a decreasing relationship.
In addition, the minimum value for x that make sense is when y = 0, that is, when the card has no money left, which is:
[tex]0=-\frac{3}{2}x+30\\-30=-\frac{3}{2}x\\x=\frac{60}{3}=20[/tex]
Therefore, the maximum value for x that makes sense to the problem is x = 20, that is, after washing 20 cars.
