Unable to solve.

[redsierra]

hello all, I am new to this forum and although I am a senior citizen, I still find difficult maths fascinating. My problem which I have been on it for the last 4 hours and unable to solve is:
Tom has three rabbits called Rob, Billy and Jerry. Each rabbit weights different.
Rob and Billy weigh 6 kilo
Billy and Jerry weigh 9 kilo
Rob and Jerry weigh 11 kilo
What is the weight of each rabbit?

All the help is appreciated. Thanks. :!:

 

[tkhunny]

R = Weight of Rob
B = Weight of Billy
J = Weight of Jerry

"Rob and Billy weigh 6 kilo"

R + B = 6

"Billy and Jerry weigh 9 kilo"

B + J = 9

"Rob and Jerry weigh 11 kilo"

R + J = 11

Now, you have three equations and three variables. This should be enough to solve with a few quick substitutions.

 

[Deleted member 4993]

R = Weight of Rob
B = Weight of Billy
J = Weight of Jerry

"Rob and Billy weigh 6 kilo"

R + B = 6 ......................................................(1)

"Billy and Jerry weigh 9 kilo"

B + J = 9......................................................(2)

"Rob and Jerry weigh 11 kilo"

R + J = 11....................................................(3)

Now, you have three equations and three variables. This should be enough to solve with a few quick substitutions.

Or you could use method of elimination.

Subtract (1) from (2) to get ? J - R = 3................(4)

Add (3) and (4) to get ? 2*J = 14 ? J = 7 (Jerry is the FAT one)

Then of course use this value of 'J' in (2) and (3) to get the others.

 

[Denis]

[1]Rob and Billy weigh 6 kilo
[2]Billy and Jerry weigh 9 kilo
[3]Rob and Jerry weigh 11 kilo

You can solve this by "looking"!
Look at [1] and [2]: Billy being in both, then Jerry weighs 3 more than Rob; OK?
So J = R + 3
Substitute that in [3]:
R + R+3 = 11
OK?

 

[redsierra]

Hi guys,
Problem solved with your help.
Thanks a lot.

 

[soroban]

Hello, redsierra!

Here's another "eyeball" approach.

Tom has three rabbits called Rob, Billy and Jerry. .Each rabbit weighs different.
Rob and Billy weigh 6 kilo.
Billy and Jerry weigh 9 kilo.
Rob and Jerry weigh 11 kilo.
What is the weight of each rabbit?

\(\displaystyle \text{We have: }\:\begin{Bmatrix}R + B \qquad &=& 6 & [1] \\ \quad\;\; B + J &=& 9 & [2] \\ R \quad\;\; + J &=& 11 & [3] \end{Bmatrix}\)

\(\displaystyle \text{Add [1], [2] and [3]: }\:2R + 2B + 2J \:=\:26 \quad\Rightarrow\quad R + B + J \:=\:13\;\;[4]\)


\(\displaystyle \text{Since }[1]\;R+B \:=\:6,\)
\(\displaystyle \text{ then [4] becomes: }\:6 + J \:=\:13 \quad\Rightarrow\quad J \:=\:7\)

\(\displaystyle \text{Then [2] becomes: }\:B + 7 \:=\:9 \quad\Rightarrow\quad B \:=\:2\)

\(\displaystyle \text{And [3] becomes: }\:R + 7 \:=\:11 \quad\Rightarrow\quad R \:=\:4\)