SOLUTION: Antonio is 2 years older than Carrie. In 6 years the sum of their ages will be 74. How old is Antonio now

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Question 1170865: Antonio is 2 years older than Carrie. In 6 years the sum of their ages will be 74. How old is Antonio now
Found 3 solutions by math_tutor2020, ikleyn, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

A = Antonio's age right now
C = Carrie's age right now
A = C+2 since Antonio is 2 years older than Carrie


A+6 = Antonio's age 6 years from now
C+6 = Carrie's age 6 years from now

Add the future age expressions and set that equal to 74
(A+6)+(C+6) = 74
A+6+C+6 = 74
A+C+12 = 74
A+C+12-12 = 74-12
A+C = 62

Then plug in A = C+2 to help solve for C
A+C = 62
C+2+C = 62
2C+2 = 62
2C+2-2 = 62-2
2C = 60
2C/2 = 60/2
C = 30

Carrie is currently 30 years old.

A = C+2
A = 30+2
A = 32

Answer: Antonio is currently 32 years old.
Answer by ikleyn(52909)   (Show Source): You can put this solution on YOUR website!
.

            It is a good problem to solve it mentally by reasoning,
            applying and exercising your common sense. 


Since the sum of their ages will be 74 in 6 years, the sum of their ages now is  74 - 6 - 6 = 62 years.


Now divide 62 by 2 to get the average of their ages  62/2 = 31 year.


The last step is to increase 31 by 1 unit to get 32 years for the older (Antonio)

and to decrease 31 by 1 unit to get 30 years for the younger (Carrie).



    By adding 1 to and subtracting 1 from 31, we provide the required difference of 2 years between the two.



ANSWER.  Antonio is 32 years old now.



Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!

Antonio is 2 years older than Carrie. In 6 years the sum of their ages will be 74. How old is Antonio now
As the ages of the 2, sum to 74 in 6 years' time, it follows that their ages NOW sum to 74 - 2(6) = 74 - 12 = 62

By letting Antonio's age be A, we find that Carrie's is A - 2

We then get: A + A - 2 = 62

2A = 64

Antonio, or  

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