Answer: Nora is 13 years old and her father is 65 years old.
Let's say that Nora is x years old. We know that her father is 5 times older than her. x times 5 is 5x, so her father is 5x years old. Since it is given that the sum of their ages is 78, we can put together this:
Nora's age + her father's age = 78 years
Substituting Nora's age for x and her father's age for 5x, we get this equation:
x + 5x = 78
x combined with 5x is equal to 6x, so:
6x = 78
If 6x is equal to 78, then 6x divided by 6 is equal to 78 divided by 6. This is done using the division property of equality.
6x/6 = 78/6
After calculating, we get this:
x = 13
x is Nora's age, so she is 13 years old. However, her father is 5 times older than her, and 13 times 5 is equal to 65. Nora's father is 65 years old.
