The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A? 

The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?

C is 12 years younger than A.

According to the given information:

A + B = B + C + 12 (The total age of A and B is 12 years more than the total age of B and C)

Now, to find the age difference between A and C:

We'll solve for C in terms of A and B from the equation above:

A + B = B + (A - C) + 12

Now, let's simplify:

A + B = B + A - C + 12

We can cancel out B from both sides:

A = A - C + 12

Now, we'll isolate C:

C = 12

So, C is 12 years younger than A.

Age Word Problems in Algebra

Age word problems in algebra typically involve determining the age of individuals at different points in time or comparing the ages of different people. Let's go through a couple of examples:

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Example 1: Tom is 5 years older than twice the age of his sister. The sum of their ages is 35. How old is each?

Let's denote:

• T as Tom's age
• S as Tom's sister's age

From the given information, we can set up two equations:

1. T = 2S + 5 (Tom is 5 years older than twice his sister's age)
2. T + S = 35 (The sum of their ages is 35)

Now, we can solve this system of equations. Let's start by substituting the expression for T from equation 1 into equation 2:

(2S + 5) + S = 35 3S + 5 = 35 3S = 30 S = 10

Now, we can find Tom's age using equation 1:

T = 2S + 5 T = 2(10) + 5 T = 20 + 5 T = 25

So, Tom is 25 years old and his sister is 10 years old.

Example 2: Ten years ago, Karen was twice the age of her sister. If the sum of their ages is 50 now, how old is each?

Let's denote:

• K as Karen's current age
• S as Karen's sister's current age

From the given information, we can set up two equations:

1. K - 10 = 2(S - 10) (Ten years ago, Karen was twice her sister's age)
2. K + S = 50 (The sum of their ages is 50 now)

Now, let's solve this system of equations. First, simplify equation 1:

K - 10 = 2S - 20 K = 2S - 10

Now, substitute this expression for K into equation 2:

(2S - 10) + S = 50 3S - 10 = 50 3S = 60 S = 20

Now, we can find Karen's age using equation 2:

K + 20 = 50 K = 50 - 20 K = 30

So, Karen is currently 30 years old and her sister is 20 years old.