Ezra takes jogs throughout the week for exercise. One jog around his neighborhood is 2 miles long, and one jog on his favorite trail is 3.5 miles long. Ezra's goal is to jog at least 15 miles this week.
Which pairs (n,t) represent possible numbers of neighborhood jogs and trail jogs that would let Ezra meet his goal?
a) ( 4,2)
b) (0,5)
c) (1,4)
d) (-2,6)
Since each neighborhood jog is 2 miles and each trail jog is 3.5 miles, we can set up the equation n(2) + t(3.5) ≥ 15, where n is the number of neighborhood jogs and t is the number of trail jogs.
Now we can plug in the given pairs:
a) (4,2) -> 4(2) + 2(3.5) = 8 + 7 = 15 -> This pair would allow Ezra to meet his goal.
b) (0,5) -> 0(2) + 5(3.5) = 0 + 17.5 = 17.5 -> This pair would also allow Ezra to meet his goal.
c) (1,4) -> 1(2) + 4(3.5) = 2 + 14 = 16 -> This pair would not allow Ezra to meet his goal.
d) (-2,6) -> -2(2) + 6(3.5) = -4 + 21 = 17 -> This pair would also not allow Ezra to meet his goal.
Therefore, the pairs that represent possible numbers of neighborhood jogs and trail jogs that would let Ezra meet his goal are:
a) (4,2)
b) (0,5)