Question

A company can send a maximum of 40 workers to complete a

task. The manager needs to limit the total cost of the workers
within $1000. He needs to pay $30 and $20 to each female
and male worker for this task respectively. Write a system of
inequalities to express this situation. What is the least possible
number of male workers the manager should send to meet the
requirements?
male workers

Answer 1

20

Explanation:

For the sake of the problem, let's make female workers "x" and male workers "y".

x+y<40 This equation shows that the total number of workers has a max of 40.

30x+20y<1,000 This equation shows that the total cost the manager pays ($30 to each woman, $20 to each man) has a max of $1,000.

Now you can solve for x and y.

X+y<40

-y -y

X<-y+40

Substitute -y+40 in for X in the second equation

30(-y+40)+20y<1,000

-30y+1200+20y<1,000 Distribute

-10y+1,200<1,000 Combine like terms

-10y<-200 Subtract 1,200

y>20 Divide by -10; flip the sign

Since y>20, and y=male workers, you now know that the minimum

number of male workers he should send is 20