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Systems of Equations : Five Word Problems

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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.

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Solution Summary

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

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Let there are x hens (2 feet) and y rabbits (4 feet).
x+y = 50 ....(1)
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

Let there are x flies and y spiders. Flies have 6 feets and spiders have 8 feets.
x+y = 42 ..(1)
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 provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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