The Cat and Turtle Problem

Starting equations. "T" stands for "table", "B" stands for "blue", and "G" stands for "green".

$T + B - G = 170 \\ T + G - B = 130$

Adding the two equations:

$2 T = 300 \\ T = 150$

$\text{cat + table - turtle = 170}$ $\text{[equation 1]}$

$\text{turtle + table - cat = 130}$ $\text{[equation 2]}$

$\text{Adding the two equation gives,}$

$\text{2 table = 300}$

$\text{table} = \dfrac{300}{2}=\boxed{150}$

Picture 1 :

Cat + Table - Turtle = 170 cms

Picture 2 :

Turtle + Table - Cat = 130 cms

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Step 1 : Cat + Table - Turtle + Turtle + Table - Cat = 300cms

Step 2 : Cancel out the +Cat with -Cat & cancel out the -Turtle with +Turtle

Step 3 : 2(Table) = 300cms

Step 4 : Table = 150cms

Height difference between Cat and Turtle (when Turtle is down) = 170 cm

Height difference between Turtle and Cat (when Cat is down) = 130 cm.

Adding the values = 130 +170= 300 cm

Then dividing by 2= $\frac{300}{2}$ =150 cm.

Hence, height of table is 150 cm.

Also, using intuition, you can answer this question, since options have been provided.

Simple, the height of the table is less than 170 cm and more than 130 cm. There was just a single option - 150 cm :)

A better solution would be this: (130 + 170) : 2 = 150

Let H = height of the table C = height of the cat T = height of the tortoise , Given >> H = 170 - C + T and H = 130 - T + C So, 170 - C + T = 130 -T + C 40 = 2 ( -T + C ) => >> H = 130 + 40 / 2 = 150

We create the following system:
Cat + table - turtle = 170
Turtle + table - cat = 130

Table = 170 - cat+ turtle
Table = 130 + cat - turtle

We obtain an easy equation by putting the two members together:
170 - cat + turtle = 130 + cat - turtle

40= 2 cat - 2 turtle

20 = cat - turtle

Cat = 20 + turtle

We substitute the value of “cat” to the first instance:
20 + turtle + table - turtle = 170

20 + table = 170

Table = 170-20 = 150cm

T+C-G=170 T+G-C=130

Subtract the two equations and you get:

2(C-G)=40 Therefore C-G is 20.

T+(C-G)=170 T+20=170 T=150

Let x be height of turtle, y be height of cat and h be height of table Then from 1st picture we have

h + y = 170 + x And from 2nd picture we have

h + x = 130 + y Add these 2 equations we have

2h = 300 or h = 150

Getting the mean, we can find the height

Just keep the left hand side table on right side then consider length of the table as as a,b and c then calculate.