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

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53 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.

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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