Question

Three fathers-Paul, Johnson, and Nicolas have between them a total of 15 children of which 9 are boys. Paul has 3 girls and Johnson has the same number of boys. Johnson has 1 more child than Paul who has 4 children. Nicholas has 4 more boys than girls and the same number of girls as Paul has boys. How many boys each do Nicolas and Paul have?

Answer 1

Nicholas has 5 boys, and Paul has 1 boy

Explanation:

We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:

`p + j + n = 15` (1st Equation)

`p_(g) = j_(b) = 3` (2nd Equation)

`j = p + 1 (p = 4)` (3rd Equation)

`n_(b) = n_(g) +4` (4th Equation)

`n_(g) = p_(b)` (5th Equation)

Whew! That was a lot. We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:

b = g + 4 and b + g = 6

So, we substitute the first equation into the second equation, giving us:

g + 4 + g = 6

2g = 2

g = 1

So, Nicholas has one girl, meaning he has 5 boys.

So, Nicholas has 5 boys, and Paul has 1 boy.

Hope this helped!