IQ TEST: Math, Pie, Cake, Divisions, Total, Sum, Parts, Age Problems

1. A birthday cake is to be divided and distributed such that the birthday celebrant will have a quarter share and the rest will have half as big as the celebrant's share. How many pieces was the cake divided?

find:

x = number of equal shares

solution:

TOTAL = sum of parts

1 = 1/4 + x(1/2 * 1/4)

x(1/8) = 3/4

x = 6

Cake divisions = 6 + 1 = 7


2. A school has 55 students for each teacher. If the school has a total of 2240 students and teachers, how many teachers are there?

find:

x = number of teachers

solution:

TOTAL = sum of students and teachers

2240 = 55x + x

56x = 2240

x = 40


3. Roland is twice as old as Adrienne. Twenty years ago, Roland was four times as old as Adrienne. How old is Adrienne now?

find:

A = Adrienne's age now

given:

now

A = Adrienne's age

R = Roland's age

R = 2A ---> equation 1


twenty years ago

A - 20 = Adrienne's age

R - 20 = Roland's age

R - 20 = 4(A - 20) ---> equation 2


substituting equation 1 in 2

2A - 20 = 4(A - 20)

2A - 20 = 4A - 80

2A = 60

A = 30