Question

Rico thinks of a number between 30 and 40 that is represented by

x
.
•
This number,
x
, is
3
_
4
of another number, which is represented by
y
.
•
The number represented by
y
equals
1
_
3
of another number, which is
represented by
z
.
•
The number represented by
z
is a number from 140 to 151.
•
The numbers represented by
x
,
y
, and
z
are whole numbers.
(a)
What are the values for
x
,
y
, and
z
?

Answer 1

Hello,

x,y,z∈ IN


`x=(3)/(4)*y`

`y=(1)/(3)*z`


`140<z<151\ ==>\ (140)/(3)<(z)/(3)<(151)/(3)`

`46\leq\ y\ \leq\ 50 ==>\ (46*3)/(4)\leq(3y)/(4)\leq(50*3)/(4)`

`35\ \leq\ z\ \leq\ 37`==>
x∈{35,36,37}
y∈{47,48,49}
z∈{141,144,147}

We must go futher:

if x=35 then y=4*35/3=46.666 not good , not whole
if x=36 then y=4*36/3=48 ok
if x=37 then y=37*4/3=49.333.. not good

So there is only one solution (36,48,144) for (x,y,z)

No problem with z for z=3/1*4/3*x=4x ==>whole.