SOLUTION: Mother's age is 4 times as much as the sum of the ages of her three children, but after six years her age will be only double the sum of their ages.The age of the mother is?

Question 1044715: Mother's age is 4 times as much as the sum of the ages of her three children, but after six years her age will be only double the sum of their ages.The age of the mother is?
Found 5 solutions by josgarithmetic, advanced_Learner, ikleyn, MathTherapy, somuahkata@gmail.com:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Ages now are m, x, y, z.

the six-more-years equation:

Look now again at the system:

, notice variable m and a variable expression.
, to use elimination method,

Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
.

Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
Mother's age is 4 times as much as the sum of the ages of her three children,
but after six years her age will be only double the sum of their ages. The age of the mother is?
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let M be the mother present age. Let S be the sum of her three children present age. Then M = 4S (1) ("Mother's age is 4 times as much as the sum of the ages of her three children") is your first equation. After six eqars, the mother's age will be M + 6. Each of her three children's age will be 6 ears more than their present age. Hence, the sum of their ages will be 18 years more than the current sum. It gives you the second equation M + 6 = 2(S + 18). (2) ("after six years her age will be only double the sum of their ages") To solve the system (1), (2), substitute expression (1) for M into (2). You will get 4S + 6 = 2S + 36, or 2S = 30, or S = = 15. Then M = 4S = 4*15 = 60. Mother's present age is 60 years. Not very realistic, but formally correct.

The lesson to learn: there is no need to use many variables in the solution.
Two variables is totally enough.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Mother's age is 4 times as much as the sum of the ages of her three children, but after six years her age will be only double the sum of their ages.The age of the mother is?

Let mother's age be M, and sum of children's ages, S
Then we get: M = 4S =====>
Also, M + 6 = 2(S + 6 * 3)______M + 6 = 2S + 36____M = 2S + 30 ------ eq (ii)
---- Substituting for S in eq (ii)

2M = M + 60 -------- Multiplying by LCD, 2
2M - M = 60
Mother's age, or
Answer by somuahkata@gmail.com(7)   (Show Source): You can put this solution on YOUR website!
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