The number of boys is 3 more than double the girls. Together, there are 54 students in total. How many boys and girls are there?
g + 2g + 3 = 54
3g = 51
g = 17
Let's use algebra to solve this problem step by step.
Step 1: Assign variables to the unknowns.
Let's use 'b' to represent the number of boys and 'g' to represent the number of girls.
Step 2: Translate the given information into equations.
The number of boys is 3 more than double the number of girls can be written as:
b = 2g + 3
The total number of students is 54, which can be written as:
b + g = 54
Step 3: Solve the system of equations.
Substitute the value of b from the first equation into the second equation:
(2g + 3) + g = 54
Combine like terms:
3g + 3 = 54
Subtract 3 from both sides:
3g = 51
Divide both sides by 3:
g = 17
Now substitute the value of g back into the first equation to find the value of b:
b = 2(17) + 3
b = 34 + 3
b = 37
Therefore, there are 37 boys and 17 girls.
To find the number of boys and girls, we can set up a system of equations based on the given information.
Let's assume the number of girls is x.
According to the given information, the number of boys is 3 more than double the girls, which can be expressed as: 2x + 3.
The total number of students is 54, so the equation can be written as:
x + (2x + 3) = 54
Simplifying the equation, we have:
3x + 3 = 54
Subtracting 3 from both sides, we get:
3x = 51
Dividing both sides by 3, we get:
x = 17
Therefore, there are 17 girls (x) and the number of boys is:
2x + 3 = 2(17) + 3 = 34 + 3 = 37
So, there are 17 girls and 37 boys in total.