Final answer:
The rancher experienced a 20% decrease in the number of cattle when the herd size was reduced from 150 head to 120 head.
Step-by-step explanation:
To calculate the percent of decrease in the number of cattle, we need to find out by how much the herd size decreased and then calculate what percentage that decrease represents of the original number of cattle. The formula to calculate the percentage decrease is: (Initial Amount - New Amount) / Initial Amount x 100.
First, we determine the decrease in herd size: 150 head (initial amount) - 120 head (new amount) = 30 head (decrease in cattle).
Next, we calculate the percent of decrease: (30 / 150) x 100 = 20%.
Therefore, the rancher's herd decreased by 20% when it went from 150 head to 120 head of cattle.