The total length of cable that is needed for the installation of the lighting in the new apartments is calculated by multiplying the number of apartments and the length of cable needed for each apartment. The calculation is shown below.
L = (12 apartments)(60 m/apartment) = 720 meters of cable
As given in the problem, each spool holds 100 meters of cable. The number of spools needed is therefore calculated by dividing the total length by the length of cable per spool as shown below.
S = (720 meters of cable) / (100 meters/spool)
S = 7.20 spools
Hence, the smallest number of new spools that Ted will need for this job is equal to 8 spools.