A Is Two Year's Older Than B Who Is Twice as Old as C. If the Total of the Ages of A, B and C Be 27, Then How Old Is B?

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, Then How old is B?

Let's denote the ages of A, B, and C as follows:

• A's age = x
• B's age = y
• C's age = z

According to the given information:

1. A is two years older than B: x = y + 2
2. B is twice as old as C: y = 2z
3. The total of their ages is 27: x + y + z = 27

Solution: Substituting x = y + 2 and y = 2z into the equation x + y + z = 27, we get:

(y + 2) + y + z = 27

2y + z + 2 = 27

Now, let's substitute y = 2z into the equation above:

2(2z) + z + 2 = 27

4z + z + 2 = 27

5z + 2 = 27

5z = 25

z = 5

Now that we have found C's age as 5, we can find B's age using the equation y = 2z:

y = 2 * 5 = 10

Finally, using the relationship x = y + 2, we can find A's age:

x = 10 + 2 = 12

So, A is 12 years old, B is 10 years old, and C is 5 years old.

Age Problems in Mathematics

Age problems are a common type of word problem in mathematics, especially at the elementary and middle school level. They involve using algebra to represent the ages of different people and then solving equations to find the unknown ages.

Here are some key things to know about age problems:

Concepts involved:

• Using variables: Each person's age is represented by a variable, usually denoted by letters like x, y, or z.
• Relating ages: The problem will provide information about how the ages are related, such as age differences, ratios, or sums.
• Setting up equations: Based on the information provided, you need to translate the problem into an equation or system of equations.
• Solving the equations: Use algebraic techniques like substitution, elimination, or factoring to solve for the unknown variables.

Tips for solving age problems:

• Read carefully: Make sure you understand all the information given in the problem.
• Identify the unknowns: What are you trying to find (e.g., someone's current age, their age in the future or past)?
• Choose variables: Assign variables to represent the unknowns.
• Write down the relationships: Translate the information about age differences, ratios, or sums into equations.
• Solve the equations: Use appropriate algebraic techniques to solve for the unknowns.
• Check your answer: Make sure your answer makes sense in the context of the problem.

Examples of age problems:

• Classic age difference problem: John is twice as old as Sarah. If John is 20 years old, how old is Sarah?
• Future age problem: In 10 years, David will be 3 times as old as he is now. If he is currently 15 years old, how old will he be in 10 years?
• Age ratio problem: The ratio of Mary's age to John's age is 3:2. If Mary is 18 years old, how old is John?