1) The numbers 2, 4, 6, and 8 are a set of four consecutive even numbers. Suppose the sum of five consecutive even numbers is 320. What is the smallest of the five numbers?
2) Twelve people purchased supplies for a ten-day camping trip with the understanding that each of the twelve will get equal daily shares. They are then joined by three more people, but make no further purchases. How long will the supplies then last if the original daily share for each person is not changed?
3) Amy can mow 600 square yards of grass in 1 1/2 hours. At this rate, how many minutes would it take her to mow 600 square feet?
1) Method 1: The middle number of an odd number of consecutive numbers is always the average of the set. Then the average of the numbers is 320/5 or 64 which also is the third or middle number. Count back by twos. The required number is 60.
Method 2: Represent the middle number by n. Then the five consecutive even numbers are n - 4, n - 2, n, n + 2, and n + 4. The sum of the five numbers is 5n. Since 5n = 320, n = 64. Thus n - 4, the first number, is 60.
2) Since each person of the original group had 10 daily shares, the total supplies are equivalent to 120 daily shares. When 3 people join the group, the total number of people becomes 15. Then each person in the new group will have 120/15 or 8 daily shares. The supplies will last 8 days.
3) Method 1: 1 square yard = 9 square feet. Then 600 square yard = 600 x 9 square feet. Since 600 square feet is 1/9 of 600 x 9 square feet, the time needed to mow 600 square feet is 1/9 of the time required to mow 600 square yard. Therefore, 1/9 of 1 1/2 hours is 1/9 x 3/2 = 1/6 hour or 10 minutes.
Method 2: Since 9 square feet = 1 square yard, 1 square foot = 1/9 square yard. Then the time needed to mow 1 square foot is 1/9 of the time needed to mow 1 square yard. Therefore, 600 square feet will require 1/9 of 1 1/2 hour or 1/6 hour or 10 minutes.