Brayden is working two summer jobs, making $18 per hour lifeguarding and making $9 per hour clearing tables. in a given week, he can work no more than 19 total hours and must earn a minimum of $270. if brayden worked 14 hours lifeguarding, determine the minimum number of whole hours clearing tables that he must work to meet his requirements. if there are no possible solutions, submit an empty answer.

2 hours.

Step-by-step explanation:

Money earned for 14 hours of life-guarding = 14*18 = $252.  If he worked another 5 hours  to make the maximum of 19 he would earn 252 + 5*9

= $297  but he wants to work a minimum of hours for  a minimum of 270.

Thus we have the inequality:

252 + 9x ≤ 270

9x  ≤  18

x  ≤ 2.

So the number of hours he must do clearing tables = 2.

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step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is