I need some help please?!?
2 answers:
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Answer:
There are three possible combinations of positive integers such that a > b:
(1) a = 15 and b = 15
(2) a = 20 and b = 12
(3) a = 45 and b = 9
Step-by-step explanation:
Notice that the possible factors (different from "1") of the denominator "15" are: 3, 5, and 15.
The answer for the case a = 15 and b = 15 is obvious since :
Then the possibility of a multiple of 5 for one of the denominators (let's say 5*n) and a multiple of 3 (let's say 3*m)for the other one gives the general equation:
which should verify the following as we try to solve for one of the unknowns multiplicative factors which by the way have to be positive for the requirement given in the problem:
This last equation is very simple to analyze using integer values for "n" which would render a positive value on the right hand side, and then check from that set the ones that give an integer for the value "m".
Those found were:
For n=3, and m=5, a=15, and b=15 (the obvious solution discussed above)
For n = 4 and m = 4, a = 20, and b = 12
and for n=9 and m=3, a=45 and b = 9
Answer:
Nina practiced the viola for 11.25 hours last week.
Step-by-step explanation:
Juan practiced the violin for 9 hours last week. For each 3 hours that he practices the violin, he practices 2.5 hours of cello. So
3h violin - 2.5h cello
9h violin - xh cello
He practiced 7.5 hours of cello, the same as Nina.
For every 3 hours Nina spends practicing the viola she practices the cello for 2 hours. So:
3h viola - 2h cello
xh viola - 7.5h cello
Nina practiced the viola for 11.25 hours last week.