Question

Three neighbors – Farid, Pang and Harjit – each own 3 cars; one two-door, one
four-door and one five-door. None of the same car brand has the same number of
doors. They each have a Honda, Toyota and Mazda. Farid’s Honda has the same
number of doors as Pang’s Toyota. Harjit’s Honda has the same number of doors
as Farid’s Toyota. Farid’s Mazda is a two-door and Pang’s Mazda is a four-door.
a. Who has a five-door Mazda?
b. Who has a five-door Toyota?
c. Who has a two-door Toyota?
d. Who has a four-door Honda?
e. Who has a five-door Honda?
f. Who has a two-door Honda?
g. Please show how you get the answers.

Answer 1

PH = Numbers of doors on Pang’s Honda

PT = Numbers of doors on Pang’s Toyota

PM = Numbers of doors on Pang’s Mazda

FH = Numbers of doors on Farid’s Honda

FT = Numbers of doors on Farid’s Toyota

FM = Numbers of doors on Farid’s Mazda

HH = Numbers of doors on Harjit’s Honda

HT = Numbers of doors on Harjit’s Toyota

HM = Numbers of doors on Harjit’s Mazda


Cars of each owner has together 11 doors:

one two-door + one four-door + one five-door = 2 + 4 + 5 = 11 doors

So you have system of equations:

FH + FT + FM = 11

PH + PT + PM = 11

HH + HT + HM = 11


Farid’s Honda has the same number of doors as Pang’s Toyota mean:

FH = PT

Harjit’s Honda has the same number of doors as Farid’s Toyota mean:

HH = FT

Farid’s Mazda is a two-door mean:

FM = 2

Pang’s Mazda is a four-door mean:

PM = 4


Put this values in the initial system:

PT + FT + 2 = 11

PH + PT + 4 = 11

FT + HT + HM = 11


Your system become:

PT + FT = 9

PH + PT = 7

FT + HT + HM = 11


First equation:

PT + FT = 9

PT = 9 - FT

One car has 5 doors, other has 4 doors.

PT = 5

FT = 4

The solution PT = 4 , FT = 9 - PT = 9 - 4 = 5 is not possible because Pang’s Mazda has four doors ( PM = 4 ) so in that case Pang’s Toyota also will bee have four-door cars.

In that case, Pang would have two four-door cars.


Second equation:

PH + PT = 7

One car has 5 doors, other has 2 doors.

PH = 2

PT = 5

The solution PH = 5 , PT = 2 is not possible because
Pang still has Toyota with five doors ( PT = 5 )

In that case, Pang would have two five-door cars.


In the initial system of equations:

FH + FT + FM = 11

FH + 4 + 2 = 11

FH + 6 = 11

FH = 5


Third equation:

FT + HT + HM = 11

4 + HT + HM = 11

Subtract 4 to both sides

HT + HM = 7

One car has two doors and the other five doors.

HT = 2

HM = 5

The solution HT = 5 , HM = 2 is not possible because
Pang’s Toyota is five-door car ( PT = 5 )

None of the same car brand has the same number of doors.

Therefore Harjit’s Toyota can’t have five doors.


In the initial system of equations:

HH + HT + HM = 11

HH + 2 + 5 = 11

HH + 7 = 11

HH = 4


Answers:

a. Harjit , because HM = 5

b. Pang, because PT = 5

c. Harjit, because HT = 2

d. Harjit , because HH = 4

e. Farid, because FH = 5

f. Pang, because PH = 2