Question

Eric's grandfather is 57 years older than Eric. Three years from now, Eric's grandfather will be 4 times as old as Eric is at that time. How old is Eric's grandfather?

Answer 1

To find Eric's grandfather's age, algebraic equations are set up using the given relationships. Eric's grandfather is found to be currently 73 years old by solving these equations.

Step-by-step explanation:

To solve the problem of determining Eric's grandfather age, we need to establish a relationship between Eric's current age and that of his grandfather, using algebraic expressions. Let's assume Eric's age is E and his grandfather's age is G. From the question, we know the following:

• Eric's grandfather is 57 years older than Eric: G = E + 57.
• In three years, Eric's age will be E + 3, and his grandfather's age will be G + 3.
• At that point, Eric's grandfather will be four times Eric's age: G + 3 = 4(E + 3).

Now we can set up the equations to solve for E and G:

1. G = E + 57
2. G + 3 = 4(E + 3)

Substitute G from the first equation into the second equation:

1. E + 57 + 3 = 4(E + 3)
2. E + 60 = 4E + 12
3. 60 - 12 = 4E - E
4. 48 = 3E
5. E = 16

Now we can find Eric's grandfather's age:

• G = 16 + 57
• G = 73

Therefore, Eric's grandfather is currently 73 years old.