Question

Three individuals are named P, Q, and R. Together they have a total of fifteen children, of which nine are boys. P has three girls and Q has the same number of boys. Q has one more child than P, who has four children. R has four more boys than the number of girls of P. The number of girls of R is equal to the number of boys of P. How many boys do R and P have?

• A. R = 3, P = 3
• B. R = 4, P = 2
• C. R = 5, P = 1
• D. R = 2, P = 4

Hint:

Break down the problem using logical steps, and use the given conditions to form equations that will help you calculate the unknown values.

Answer 1

The Correct Option is B

Step 1: Establishing equations based on the given data.
- Total number of children = 15 - Total number of boys = 9 - P has 3 girls and 4 children, so P must have 1 boy (since P has 4 children in total).
- Q has the same number of boys as P, so Q also has 1 boy. Since Q has 1 more child than P, Q must have 5 children. Thus, Q has 4 girls.
- R has 4 more boys than the number of girls P has. Since P has 3 girls, R must have 7 boys (4 more than 3).

Step 2: Checking the conditions.
- The number of girls R has is equal to the number of boys P has. Since P has 1 boy, R must have 1 girl. Thus, R has 7 boys and 1 girl.

Step 3: Verifying the total.
The total number of boys is 9, which matches the total number of boys in the problem. The total number of children is 15, which matches the total number of children in the problem. Thus, the solution is correct.

Step 4: Conclusion.
Therefore, the correct answer is (B) R = 4, P = 2.