In Ms. Salmon’s 4th grade class, there are half as many boys as there are girls. There are 30 students all together. How many are boys? How many are girls? Explain how you solved the problem
g = 2b
b + 2b = 30
b = 10
g = 20
it was fine thanks
To solve this problem, we can start by letting "x" represent the number of girls in Ms. Salmon's class. Since there are half as many boys as girls, we can say that the number of boys is equal to half of the number of girls, which can be represented as "x/2."
According to the problem, there are 30 students all together. So, the total number of students is equal to the sum of the number of boys and the number of girls: x + x/2 = 30.
To solve this equation, we can multiply through by 2 to remove the fraction: 2(x + x/2) = 2(30), which simplifies to 2x + x = 60.
Combining like terms, we have 3x = 60. To solve for x, we divide both sides of the equation by 3: x = 60/3.
Therefore, x = 20, which represents the number of girls in Ms. Salmon's class. To find the number of boys, we can substitute x back into the equation for the number of boys: x/2 = 20/2 = 10.
Therefore, there are 10 boys and 20 girls in Ms. Salmon's 4th-grade class.
To solve this problem, we need to follow a logical step-by-step process. Here's how we can determine the number of boys and girls in Ms. Salmon's 4th-grade class:
Step 1: Define variables:
Let's represent the number of girls as "G" and the number of boys as "B."
Step 2: Set up the given conditions as equations:
According to the problem, the number of boys is half the number of girls. Mathematically, this translates to: B = (1/2)G.
Step 3: Form a second equation using the total number of students:
We know that there are 30 students in total. So we can add the number of boys and girls together: B + G = 30.
Step 4: Solve the system of equations:
Now we have a system of two equations that we can solve simultaneously to find the values of B and G.
We'll use the first equation, B = (1/2)G, to substitute the value of B in the second equation, B + G = 30:
(1/2)G + G = 30
(3/2)G = 30
Multiplying both sides by 2/3 (the reciprocal of 3/2):
G = (30 * 2/3)
G = 20
Once we have the value of G, we can substitute it back into the first equation to find B:
B = (1/2) * 20
B = 10
Therefore, there are 10 boys and 20 girls in Ms. Salmon's 4th-grade class.