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24 votes
24 votes
the length c.d akers rectangular garden is 37 shorter than six times. the width. if the perimeter.of.his garden is 164 feet. what are the dimensions of mr.alers garden

User Geir Bostad
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1 Answer

25 votes
25 votes

4.

The farmer has 40 more chickens than cows

Ten fewer pigs than cows

Twenty fewer sheep than chickens

Four horses

The total animals in the farm are 110.

First symbolize the expressions, for this I'm going to use the following letters:

x= cows

y=chickens

z=pigs

w=sheeps

u= horses

"The farmer has 40 more chickens than cows"→ y=x+40

"Ten fewer pigs than cows"→ z=x-10

"Twenty fewer sheep than chickens"→ w= y-20

"Four horses"→ u=4

Total animals on the farm:

T=x+y+z+w+u

T=110

As you can see there are 4 unknowns in the equation, considering that x is the one most repeated, first thing is to express all the others in terms of it.

Using y=x+40, I'll rewrite the formula for w in terms of x:

w=y-20

w=(x+40)-20 \You can take the parenthesis away

w=x+40-20

w=x+20

Now you have to replace each one on the formula for T

T=x+y+z+w+u

110=x+(x+40)+(x-10)+(x+20)+4


\begin{gathered} 110=x+x+40+x-10+x+20+4 \\ 110=4x+54 \\ 4x=56 \\ x=14 \end{gathered}

There are 14 cows in the farm.

Next you can calculate the rest of the animals.

Chickens:

y=x+40= 14+40= 54 chickens

Pigs

z=x-10=14-10= 4 pigs

Sheep

w=x+20= 14+20= 34 sheep

User APerson
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