Lawrence has two part-time jobs, one at a movie theater and one at a pet store. He is paid by the hour at each job. Last week, he worked 10 hours at the movie theater and 8 hours at the pet store and earned a total of $152.50. The week before, he worked 8 hours at the movie theater and 12 hours at the pet store and earned a total of $171.00.
a. Determine how much Lawrence earns per hour at the pet store. Show all of your work.
b. Next week, Lawrence wants to earn at least $168.00. He is scheduled to work 6 hours at the pet store. Write and solve an inequality to find the minimum number of hours he needs to work at the movie theater in order to earn at least $168.00. Show all of your work.
Thanks In advance
a. Determine how much Lawrence earns per hour at the pet store. Show all of your work.
b. Next week, Lawrence wants to earn at least $168.00. He is scheduled to work 6 hours at the pet store. Write and solve an inequality to find the minimum number of hours he needs to work at the movie theater in order to earn at least $168.00. Show all of your work.
Thanks In advance
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P is the variable describing the amount of # made/hour in the pet store
M is the variable describing the amount of # made/hour in the movie theater
Equation 1:
10M+8P=152.5
Equation 2:
8M+12P=171 now if we solve for M in this equation we get 8M = 171-12P --------> M=(171-12P)/8
Now we substitute this into equation 1.
10[(171-12P)/8]+8P=152.5 ------> (1710-120P)/8+8P+152.5---> [(1710-120P)+64P]/8=152.5 now we multiply both sides with 8.
1710-120P+64P= 1220 ----------> 1710-1220=120P-64P-->490=56P-----------> P=8.75 dollars/hour
10M + 8P=152.5---> 10M=152.5-8P = 152.5-70 = 82.5----------> M=8.25dollars per hour
Ans for part a: pay in pet store is 8.75dollars/hours and the pay for the movie is 8.25dollar/hours
b) mh is the variable describing the numbers of hours worked in the movie
6P+(mh)M=168------->(mh)(8.25)=168-6(8… = 168-52.5 = 115.5 -----> mh = 115.5/8.25 = 14 hours
therefore in order to make 168 dollar while working 6 hours in the movie theather then lawrence must work at least 14 hours!
M is the variable describing the amount of # made/hour in the movie theater
Equation 1:
10M+8P=152.5
Equation 2:
8M+12P=171 now if we solve for M in this equation we get 8M = 171-12P --------> M=(171-12P)/8
Now we substitute this into equation 1.
10[(171-12P)/8]+8P=152.5 ------> (1710-120P)/8+8P+152.5---> [(1710-120P)+64P]/8=152.5 now we multiply both sides with 8.
1710-120P+64P= 1220 ----------> 1710-1220=120P-64P-->490=56P-----------> P=8.75 dollars/hour
10M + 8P=152.5---> 10M=152.5-8P = 152.5-70 = 82.5----------> M=8.25dollars per hour
Ans for part a: pay in pet store is 8.75dollars/hours and the pay for the movie is 8.25dollar/hours
b) mh is the variable describing the numbers of hours worked in the movie
6P+(mh)M=168------->(mh)(8.25)=168-6(8… = 168-52.5 = 115.5 -----> mh = 115.5/8.25 = 14 hours
therefore in order to make 168 dollar while working 6 hours in the movie theather then lawrence must work at least 14 hours!
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10M + 8P = 152.50
8M + 12P = 171.00
Whence P = [5*171.00 -- 4*152.50] / [5*12 -- 4*10] = 12.25
Pet @ $12.25 per hour ANSWER
10M = 152.50 -- 8P = 152.50 -- 8*12.25 = 54.50 giving M = 5.45
6P + nM = 168 giving n = [168 -- 6P] / M = [168 -- 6*12.25] / 5.45 = 17.339
Minimum 18 hours at Movie ANSWER
8M + 12P = 171.00
Whence P = [5*171.00 -- 4*152.50] / [5*12 -- 4*10] = 12.25
Pet @ $12.25 per hour ANSWER
10M = 152.50 -- 8P = 152.50 -- 8*12.25 = 54.50 giving M = 5.45
6P + nM = 168 giving n = [168 -- 6P] / M = [168 -- 6*12.25] / 5.45 = 17.339
Minimum 18 hours at Movie ANSWER