Satish is making school spirit keychains, which consist of a sequence of n beads on a string. he has blue beads and gold beads. how many unique keychains can he make with exactly k ≤ n blue beads?

David and alton are training for a race. they spend 35 minutes stretching and then go on a 5 mile practice run. david runs at a pace of 7 min/mile. alton runs at a pace of 8 min/mile. write an equation for each runner that shows the total length of their workout. then solve each equation showing your work