The bus fare in a city is $ 1.75 People who use the bus have the option of purchasing a monthly coupon book for $ 35.00 With the coupon book, the fare is reduced to $0.50. How many times must someone use the bus so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book?

28 times

Step-by-step explanation:

Create an equation where x represents the number of times the bus is used:

1.75x = 0.5x + 35

Solve for x:

1.75x = 0.5x + 35

1.25x = 35

x = 28

So, the bus has to be used 28 times for the prices to be the same.

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