A school district has two high schools: Lowell, serving 1,715 students, and Fairview, serving 7,364. The district could only afford to hire 13 guidance counselors and apportions them using Lowndes’ method. The following year, the district expands to include a third school, serving 2,989 students, and hires four additional counselors. After hiring that many new counselors, the district recalculates the reapportion using again Lowndes' method. Which apportionment issue may result from this apportionment?

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.