Question

Joanne works two jobs to pay for college. She tutors for $25 per hour and also works as a receptionist for $12 per hour. Due to her class and study schedule, Joanne is only able to work up to 25 hours per week, but must earn at least $200 per week. If t represents the number of hours Joanne tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario?

Answer 1

t + r ≥ 25
25t + 12r = 200

t + r ≤ 25
25t + 12r ≤ 200

t + r ≤ 25
25t + 12r ≥ 200

None of the systems shown represent this scenario.

Answer 2

@jim_thompson5910 hi could you help me with this?

Answer 3

t is the number of hours she tutors
r is the number of hours she works as a receptionist

Answer 4

so t+r is the total time for tutoring and receptionist work combined

Answer 5

is this total amount of time less than 25? or greater than 25?

Answer 6

um greater than?

Answer 7

remember "Joanne is only able to work up to 25 hours per week"

Answer 8

so can she work more than 25 hours?

Answer 9

no

Answer 10

so this means that t+r has to be less than 25 (or it can be equal to 25)

but it cannot be any greater

Answer 11

so t + r ≤ 25

Answer 12

if she earns $25 an hour for tutoring and $12 an hour for receptionist work, then she earns a total of 25t + 12r dollars

this amount must be at least $200

Answer 13

so what does that mean?

Answer 14

25t + 12r=200 ....?

Answer 15

close

Answer 16

at least 200 means 200 or more

Answer 17

so wait...what do i do?

Answer 18

25t + 12r can be equal to 200 or it can be greater than 200

Answer 19

so is it

25t + 12r ≤ 200

OR

is it

25t + 12r ≥ 200

Answer 20

25t + 12r ≥ 200 ...

Answer 21

yep

Answer 22

put this all together to get this system


t + r ≤ 25
25t + 12r ≥ 200