Hari & Farid have $180 altogether. Hari & Peter have $340 altogether. Peter has 6 times as much money (cont'd)

Question

as Farid. How much money does Hari have ?

Answer 1

h + f = 180
h + p = 340
p = 6f

h + 6f = 340
180 - f + 6f = 340
5f = 160
f = 32

h + f= 180
h + 32 = 180
h = 148

hari has 148 dollars

Answer 2

Let's translate this to a system of equation:

Hari and Farid have $180 altogother:
H + F = 180 eqn(1)

Hari and Peter have $340 altogether:
H + P = 340 eqn(2)

Peter has 6 times as much money as Farid;
P = 6F eqn(3)

substitute eqn(3) to eqn(2):
H + 6F =340

and subtract eqn(1) to this new equation:
H + 6F =340
-H - F = -180
--------------------
5F = 160
F = 32
going back to eqn(1) and substitute the value of F:
H + F = 180
H + 32 = 180
H = 148

Answer 3

340 - 6x = 180 - x
340 = 180 + 5x
160 = 5x
x = 32
180 -32 = 148