# Systems of Equations : Five Word Problems

There are hens + rabbits. The heads = 50 the feet = 134. How many hens & how many rabbits ?

Flies + spiders sum 42 heads and 276 feet. How many of each class?

J received $1000 and bought 9 packs of whole milk & skim milk that totalled $960 - How many packs bought of each kind?

A number is composed of two integers and its sum is 9 if the order is inverted the result is equal to the given number plus 9 more units - find the number.

Determine 2 numbers such that the difference of its squares is 120 and the sum is 6.

If I have 30 coins of two kinds 5 cents and 1 cent can I have a total of 78?

A rectangle has a perimeter of 392 m calculate its dimensions if the length is 52 m longer than the width.

https://brainmass.com/math/linear-algebra/systems-equations-five-word-problems-19771

#### Solution Preview

1.)

Let there are x hens (2 feet) and y rabbits (4 feet).

Heads,

x+y = 50 ....(1)

Feets,

2x + 4y = 134

=> x + 2y = 67 ..(2)

Eqn. (2) - (1), we get,

y = 17

thereforem from Eqn. (1), x = 50 - 17 = 33

Hence, hens = 33 and rabbits = 17 --Answer

2.)

Let there are x flies and y spiders. Flies have 6 feets and spiders have 8 feets.

Heads,

x+y = 42 ..(1)

Feets,

6x+8y = 276

=> 3x+4y = 138 ...(2)

Eqn. (1)*3:

3x + 3y = 126 ....(1)*3

Eqn. (2) - (1)*3, we get,

y = 12

Therefore, from Eqn. (1) eliminate y, ...

#### Solution Summary

Five word problems are solved using systems of equations. The expert calculates the dimensions of lengths and widths.