The howard county chili cook-off ranks cooks to determine a winner. first place votes get 5 points, second place votes get 4 points, third place votes get 2 points and fourth place votes get 1 point. the winner of the cook-off received 342 points. if johnny was 31 points behind the winner and he received 40 first place votes, 5 third place votes and 1 fourth place vote, how many second place votes did he get?

25 second place votes

Step-by-step explanation:

342-31=311

first 40x5=200

third 5x2=10

forth  1x1=1

200+10+1=211

311-211=100

100/4(second)

25 second place votes

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