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) (-2,6)
b) (1,4)
c) (4,2)
d) (0,5)
To figure out the possible combinations of neighborhood jogs (n) and trail jogs (t) that would let Ezra meet his goal of jogging at least 15 miles this week, we can set up an equation:
2n + 3.5t ≥ 15
Now we can substitute the values from each pair to see which ones satisfy the equation:
a) (-2,6):
2(-2) + 3.5(6) = -4 + 21 = 17 (not ≥ 15)
b) (1,4):
2(1) + 3.5(4)= 2 + 14 = 16 (≥ 15)
This pair satisfies the equation.
c) (4,2):
2(4) + 3.5(2) = 8 + 7 = 15 (≥ 15)
This pair satisfies the equation.
d) (0,5):
2(0) + 3.5(5) = 0 + 17.5 = 17.5 (not ≥ 15)
Therefore, the pairs that represent possible numbers of neighborhood jogs and trail jogs that would let Ezra meet his goal are (1,4) and (4,2).
The answer is b) (1,4) and c) (4,2).