Helpp!! :Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $7 an hour as a library assistant
working y hours a week. She will work both jobs. She is able to work no more than 16 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs.
write an inequality to represent this,and please solve for y
WORTH 22 POINTSSSSSS

so pay=hours times pay per hour

so the babysitting job pays 4 dollers pay per hour
she works x hours
therefor the babysitting pay is 4 times x or 4x

the library job pays 7 dollars an hour
she works y hurs
therefor the library pay is 7 times y or 7y

so total pay is babysitting pay plus library pay or
4x+7y=total pay
x+y=total hours

she wants to work no more than 16 hour s aweek, means that she can work max 16 hours or
total hours<16
subsitute
x+y<16

and she wants to earn at least 80 dolars
so more than or equal to 80 dolllars
total pay >80
subsitue
4x+7y>80

so the inequalities we have are
x+y<16 and
4x+7y>80

solve for y since we want to do that
multiply the first equatl by -4
remember tha tmultipy by negative means flip sign from < to > so
-4x-4y>-64
now add to the second equation

-4x-4y>-64
4x+7y>80 +
0x+3y>16
3y>16
divide by 3
y>16/3
16/3=5 and 1/3

so she has to work more than 5 and 1/3 hours per week

basically, she will earn at least 80 dollars a week if she works at least 5 and 1/3 hours at the library and works for 16 hours total (library+babysitting)

what you should do is find the graph of the lines
x+y<16 and 4x+7y>80 and find where they intersect

the inequaltiy is 4x+7y>80 and x+y<16