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Carmen's age was twice as old as Luis was when Carmen was Luis's age. When Luis is Carmen's age, their ages will add up to 112.

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Answer to a math question Carmen's age was twice as old as Luis was when Carmen was Luis's age. When Luis is Carmen's age, their ages will add up to 112.

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Frederik
4.6
101 Answers
Let's start by representing Carmen's current age as C and Luis's current age as L.

According to the first statement, Carmen's age was twice as old as Luis was when Carmen was Luis's age, we can write an equation:

C = 2*(L - (C - L))

Next, the second statement says that when Luis is Carmen's age, their ages will add up to 112. We can express this as another equation:

L + (L + C) = 112

Now, we can solve these two equations to find the values of C and L.

Expanding the first equation:

C = 2*(L - (C - L))
C = 2*(L - C + L)
C = 2*(2L - C)
C = 4L - 2C

Moving the terms involving C to one side:

3C = 4L

Dividing both sides by 3:

C = (4/3)L

Substituting this value of C into the second equation:

L + (L + C) = 112
L + (L + (4/3)L) = 112
L + (3/3)L + (4/3)L = 112
(10/3)L = 112

Multiplying both sides by 3/10:

L = (3/10)*112
L = 33.6

Substituting this value of L back into the first equation to find C:

C = (4/3)*(33.6)
C = 44.8

Therefore, currently Carmen is 44.8 years old and Luis is 33.6 years old.

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