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One Variable Equestion - Word Problem











































Age of Shashi's mother is 12 years more than twice the age of shashi. After 8 years mothers's age will be 20 less than trice the age of Shashi. Find the present age of Shashi and his mother.
Answers- Shashi-16 years.

Please give a line by line solution.

Comments for One Variable Equestion - Word Problem

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Jul 18, 2011
Algebra 'Age' Word Problem
by: Staff


The question:

Age of Shashi's mother is 12 years more than twice the age of shashi. After 8 years mothers's age will be 20 less than trice the age of Shashi. Find the present age of Shashi and his mother.
Answers- Shashi-16 years.

Please give a line by line solution.


The answer:


M = mother’s age
X = Shashi’s age


Shashi’s mother is 12 years older than twice the age of Shashi.

M = 2X + 12

After 8 years mother’s age will be 20 less than trice the age of Shashi. (both Shashi and her mother will each be 8 years older)

M + 8 = 3(X+8) - 20



Two equations, two unknowns

M = 2X + 12

M + 8 = 3(X+8) - 20


Simplify the 2nd equation

M + 8 = 3(X+8) - 20

Use the distributive law to remove the parentheses from the right side of the equation

M + 8 = 3(X+8) - 20

M + 8 = 3X + 24 - 20

Combine like terms

M + 8 = 3X + 4


Subtract 8 from each side of the equation

M + 8 - 8 = 3X + 4 - 8

M + 0 = 3X + 4 - 8

M = 3X + 4 - 8

M = 3X - 4


The two equations can now be written:

M = 2X + 12

M = 3X - 4


To solve these equations, use the addition/subtraction method. Subtract equation 2 from equation 1:

M = 2X + 12

-(M = 3X - 4)


M = 2X + 12

-M = -3X + 4
------------------
M - M = 2X - 3X + 12 + 4


Combine like terms

M - M = 2X - 3X + 12 + 4

0 = 2X - 3X + 12 + 4

0 = - 1X + 12 + 4

0 = - X + 12 + 4

0 = - X + 16


Add +X to each side of the equation

0 + X = - X + X + 16

Combine like terms

X = - X + X + 16

X = 0 + 16

X = 16, Shashi is 16 years old


Substitute 16 for X in the 1st equation

M = 2X + 12

M = 2*16 + 12

M = 32 + 12

M = 44, Shashi’s mother’s age is 44


The final answer is:

Shashi is 16 years old
Shashi’s mother is 44 years old


Check to answers by substituting 16 for X, and the 44 for M in the original two equations:

1st equation

M = 2X + 12

44 = 2*16 + 12

44 = 32 + 12

44 = 44, OK


2nd equation

M + 8 = 3(X+8) - 20

44 + 8 = 3(16+8) - 20

52 = 3(16+8) - 20

52 = 3(24) - 20

52 = 72 - 20

52 = 52, OK



Thanks for writing.

Staff
www.solving-math-problems.com




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