Ratio, Direct and Inverse proportion

Question

1. Of the number of student ID cards issued to newly enrolled students of University of Ghana, Legon, one-third (1/3) were issued to main campus students, one-third (1/3) of what remained were also issued to City campus students, one-fourth (1/4) of what still remained to Distance Education (DE) students, and the remainder, being 15 to Diploma students. (a.) How many ID cards were issued to the newly enrolled students? (b.) How many DE students were issued the student ID cards by the University of Ghana, Legon?

 

2.Find two numbers such that if 18 is added to the first number it becomes twice the second number and if 16 is added to the second number it becomes three times the first number

 

3.If 5 Distance Education (DE) students working independently and at the same rate can solve 26 general quadratic expressions in 3 days, how many general quadratic expressions can 15 DE students solve in 150 days, given the fact that they work independently and at the same rate?

Answer 1

1)

1/3 were issued to main campus students

This leaves 2/3

Of the 2/3, 1/3 of them {(2/3)(1/3) = 2/9] were issued to City campus students

We've issued 1/3 + 2/9 = 5/9, so 4/9 of the ID cards are left.

of the 4/9, 1/4 [(4/9)(1/4) = 1/9] were issued to distance ed students

We've now issued 5/9 + 1/9 = 6/9 = 2/3, so 1/3 of the cards are left.

There were 15 issued to diploma students.  15 is 1/3 of the total; total is 15*3=45

Cards issued:

main campus: (45)(1/3) = 15

City Campus: (45)(2/9) = 10

Distance Ed: (45)(1/9) = 5

Diploma: 15

 

2)

Let X and Y be the two numbers

X+18 = 2Y

3X = Y+16

 

The first equation can be rewritten as X=2Y-18

Substitute this for X in the 2nd equation

3(2Y-18)=Y+6

6Y-54=Y+6

5Y = 60

Y = 12

X = 2Y-18 = 2(12)-18 = 6

 

3)

5 DE students solve 26 in 3 days

This means that in one day these five students solve 26/3 expressions per day

Each student solves 26/(3*5) = 26/15 questions per day

 

26/15 * 15 * 150 = 3900