SOLUTION: Maria is 5 more than thrice the age of her brother. In 8 years , the sum of their ages will be 33. How old is Maria and her brother now?

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Question 1206413: Maria is 5 more than thrice the age of her brother. In 8 years , the sum of their ages will be 33.
How old is Maria and her brother now?
Found 3 solutions by math_tutor2020, josgarithmetic, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

b = brother's present day age
3b = three times that amount
3b+5 = Maria's present day age

Add on 8 to each to fast-forward the clock.
b+8 = brother's future age
(3b+5)+8 = 3b+13 = maria's future age

Add those future ages to get 33.
This will allow us to determine b.
brother+maria = 33
(b+8)+(3b+13) = 33
4b+21 = 33
4b = 33-21
4b = 12
b = 12/4
b = 3
Her brother is currently 3 years old.

3b+5 = 3*3+5 = 14
Maria is currently 14 years old.

In 8 years they will be...
brother = 3+8 = 11
maria = 14+8 = 22
Their future age sum will be 11+22 = 33, so we have confirmed the answers are correct.
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
                  NOW            8 YEARS TO FUTURE

Maria            3y+5             3y+5+8=3y+13

Brother            y              y+8

SUM                                33


.
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Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

It can be easily solved mentally, without using equations. 

    "In 8 years, the sum of their ages will be 33."


Hence, now, or today, the sum of their ages is 33-8-8 = 33-16 = 17.


Thus, we have that Maria is 5 more than trice the age of her brother,
                   and the sum of their ages is 17.


Take 5 years away from both parts of this statement, for a moment, and will work with "corrected" Maria age.  
You will get

                  Maria is thrice the age of her brother
                  and the sum of their ages is 12.


At this point, it is easy to guess that the brother is 3 years old, while Maria's corrected age is 3*3 = 9 years.
Now return these 5 years to the Maria's age and get her true age  9+5 = 14 years.


ANSWER.  Maria is 14 years old; her brother is 3 years old.

Solved.

-------------------

Good student should know the algebra solution, shown to you by the other tutor.

It is a base and a basic.

Knowing mental solution will make your horizon wider, and will add you more confidence.



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