Math club question

Question

A math club has 100 members the number of girls is 5 less than 2x the number of boys. How many boys and How many girls

Answer 1

We know there are a total of 100 members. Let's set up a few equations to make this simple.

First: Let x = girls and y = boys.

Since there are 100 members:

Equation #1: 100 = x + y

 

We also know the relation of girls to boys, "5 less than 2x the number of boys":

Equation #2: x = 2y - 5

 

Next, we can insert it into Equation #1. This is called the substitution method.

Rearrangement: add 5 to both sides of the equation.

New Equation #2 solved for x: x = 2y - 5

Then we substitute y in equation #1 for the equation we just found:

100 = (2y - 5) + y

Now, we can solve for one variable, y.
100 = (2y - 5) + y ==> subtract 5 from both sides

105 = 2y + y ==> simplify
105 = 3y ==>divide both sides by 3 to solve for y

35 = y.

We just solved for the number of boys, now we need to find the number of girls. Use the value of y to solve for x. At this point, we can use either equation. Let's use equation #1:

100 = x + y
100 = x + 35
65 = x

We can check our answer with equation #2 by inserting both values:

 

x = 2y - 5

65 = 2(35) - 5
65 = 70 - 5
65 = 65  ==> Since this is a true statement, we know our answer is correct.

Let me know if you have any questions. I am an algebra tutor, and I would be happy to help you further.

 

Answer 2

G=Number of girls

B=Number of boys

B+G=100:sum of boys and girls is 100.

G=2*B-5:the number of girls is 5 less than twice the number of boys.

Subtract the equations to eliminate G:

B=100-2B+5

3B=105

B=105/3=35

so, there are 35 boys and 65 girls.