Devilslayer
Answered

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

?

Verified Answer :

caylus

Hello,

x,y,z∈ IN

\(x=\frac{3}{4}*y\)
\(y=\frac{1}{3}*z\)

\(140\ \frac{140}{3}<\frac{z}{3}<\frac{151}{3}\)
\(46\leq\ y\ \leq\ 50 ==>\ \frac{46*3}{4}\leq\frac{3y}{4}\leq\frac{50*3}{4}\)
\(35\ \leq\ z\ \leq\ 37\)==>
 x∈{35,36,37}
 y∈{47,48,49}
 z∈{141,144,147}

We must go futher:

if x=35 then y=435/3=46.666 not good , not whole
if x=36 then y=436/3=48 ok
if x=37 then y=374/3=49.333.. not good

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

No problem with z for z=3/14/3*x=4x ==>whole.









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