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Silmultaneous Equations

by Bodea Annette
(Nigeria)











































a woman is q yrs old while her son is p yrs old.The sum of their ages is equals to twice the difference of their ages. The product of their ages is 675.Write down the equations connecting their ages and solve the equation i order to find the ages of the woman and her son.

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Jun 13, 2011
Simultaneous Equations
by: Staff

The question:

by Bodea Annette
(Nigeria)

a woman is q yrs old while her son is p yrs old.The sum of their ages is equals to twice the difference of their ages. The product of their ages is 675.Write down the equations connecting their ages and solve the equation i order to find the ages of the woman and her son.


The answer:


a woman is q yrs old while her son is p yrs old

q = age of a woman
p = age of the woman?s son

Write the equations:

The sum of their ages is equals to twice the difference of their ages.

q + p = 2*(q - p)


The product of their ages is 675

q * p = 675


Two equations, two unknowns:

q + p = 2*(q - p)
q * p = 675



Solve for q and p using substitution

Using the 2nd equation, solve for q

q * p = 675

q * p/p = 675/p

q * 1 = 675/p

q = 675/p



simplify the 1st equation

q + p = 2*(q - p)

q + p = 2*q - 2*p

q + p + 2*p = 2*q - 2*p + 2*p

q + 3*p = 2*q - 2*p + 2*p

q + 3*p = 2*q + 0

q + 3*p = 2*q

q - q + 3*p = 2*q - q

0 + 3*p = 2*q - q

3*p = 2*q ? q

3*p = q

q = 3*p


substitute 675/p for q in the simplified version of the 1st equation:

q = 3*p

675/p = 3*p


solve for p

multiply each side of the equation by p

p*(675/p) = p*(3*p)

675*(p/p) = p*(3*p)

675*(1) = p*(3*p)

675 = p*(3*p)

675 = 3*p*p


675 = 3*p²

Divide each side of the equation by 3

675 = 3*p²

675/3 = (3*p²)/3

225 = (3*p²)/3

225 = (p²) * (3/3)

225 = (p²) * (3/3)

225 = (p²) * (1)

225 = p²

p² = 225

take the square root of each side of the equation

√(p²) = √(225)

√(p²) = √(15²)

p = 15


solve for q by substituting 15 for p in the simplified version of the 1st equation

q = 3*p

q = 3*15

q = 45


the final answer is:

the equations:

q + p = 2*(q - p)
q * p = 675

the solution (ages of the mother and son):

mother:

q = 45


son:

p = 15




Check the work. Substitute 45 for q and 15 for p in the original two equations.


1st equation: The sum of their ages is equals to twice the difference of their ages.


q + p = 2*(q - p)

45 + 15 = 2*(45 - 15)

60 = 2*(45 - 15)

60 = 2*(30)

60 = 60, OK


2nd equation: The product of their ages is 675.


q * p = 675

45 * 15 = 675

675 = 675, OK




Thanks for writing.

Staff
www.solving-math-problems.com



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