Problema Solution
Jon finds a part time job which pays $9.20 per hour and his hourly wage goes up $0.23 for accumulating 50 hours. After his first 50 hours, his wage goes up to $9.43 and then goes to $9.66 and so on.
a) How many hours should he work there that his wage is over $12?
b) If he works only 20 hours / week, how many months he has to work to get $15/hr?
Answer provided by our tutors
after 0*50 = 0 hour his wage is
a0 = 9.20
after 1*50 = 50 hour his wage is
a1 = 9.20 + 0.23
after 2*50 = 100 hour his wage is
a2 = 9.20 + 2*0.23
after n*50 = 50n hours his wage will be
an = 9.20 + n*0.23
a) How many hours should he work there that his wage is over $12?
an >= 12
9.20 + n*0.23 >= 12
by solving we find
n >= 12.2
click here to see the step by step solution of the inequality
since n is integer we find n =13 or that he must work at least 13*50 = 650 hours to get a wage over 12$
b) If he works only 20 hours / week, how many months he has to work to get $15/hr?
first will find how many hour he has to work to get wage of $15/hr
9.20 + n*0.23 >= 15
by solving we find
n >= 25.2
click here to see the step by step solution of the inequality
since n iis integer and the first integer bigger then 25.2 is 26 thus he has to work 26*50 = 1300 hr
since he works only 20 hours / week he will have to work 1300/20 = 65 weeks
1 month = 4.35 weeks
65/4.35 = 14.94 months
Jon will have to work 14.94 month to get 15$/hr.