[Quiz] Calculate the age using variables

Welcome to Math Quiz number 45! This quiz contains a set of questions that are specifically designed for fifth and sixth grade students. These questions are related to finding the ages of people given in the problem. The quiz is meant to test students’ knowledge of converting age-related problems into a set of equations and solving those equations to find the ages. Please note that calculators or online tools are not allowed to answer the questions. If you find any incorrect answers, please feel free to leave a comment. Enjoy the quiz!

1. 
10 years ago, Alice's age was four times Bob's age. If the sum of their ages now is 45, how old are they?

2. 
The sum of the ages of a brother and a sister is 36. Six years ago, the brother was two times as old as his sister. How old are they now?

3. 
A group of four friends has an average age of 25 years. If one of the friends is 40 years old, what is the average age of the remaining three friends?

4. 
The sum of the ages of two friends is 60. If one friend is twice as old as the other, how old is each friend?

5. 
If the difference between twice John's age and four times Bob's age is 30, and the sum of their ages is 45, how old is John?

6. 
A teacher is currently four times as old as her student. In 8 years, she will be three times as old as her student. How old is the teacher now?

7. 
A father is currently three times as old as his son. In 5 years, the father will be twice as old as his son. How old is the son now?

8. 
Fifteen years ago, a mother was six times as old as her daughter. If the sum of their ages now is 58, how old is each person?

9. 
The sum of the ages of two sisters is 40. If one sister is 6 years older than the other, how old is each sister?

10. 
The ages of two friends are in the ratio 5:7. If the sum of their ages is 48, how old is each friend?

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