How many students in the class?

Question

In a class, 2/3 of the boys and 1/6 of the girls wear spectacles.

An equal number of boys and girls do not wear spectacles.

If there are 9 more boys than girls in the class, how many students are there in the class?

Answer 1

Hello Zul,

We solve such math problems by using equations. One important step is to understand the story in the problem, then write out that story in our equations. We then can solve the equations thru our related mathematical knowledge.

We are asked about the total number of students in the class. There are many ways we can get this total number, such as 1) total number of girls and total number of boys, or 2) students who wear spectacles and students who do not wear spectacles, or even 3) students whose birthday fall in Nov and students whose birthday in other months ….. We then just take a sum of the breakdowns.

However, among many ways we listed above, or even many other ways we can imagine how the students in the class can be grouped into, we do not have related information. Such as, the story in the problem mentioned nothing to us about students’ birthday, and if we go on that route, we will get stuck. Hence, we need to try to get ourselves closer to the info that we can find from the story.

With such said, let’s try to get the total number of students by finding out the number of girls and the number of boys, then sum up.

Remember, our first goal is simply to write out the story thru equations. To do that, we need to use some symbols to represent some unknown numbers mentioned in the story. Here, let’s use x to represent the number of girls, and y for the number of boys.

Alright.

Step 1:

We know “2/3 of the boys and 1/6 of the girls wear spectacles”. We take a note on our scratch paper: 2/3 y and 1/6 x wear spectacles.

Step 2:

We also know “An equal number of boys and girls do not wear spectacles.” How do we write this part of story with a math equation? This part of story gives a way to build our equation. We just need to figure out a way to represent what on the left side, and what on the right side of the “=” sign.

How do we represent the number boys who do not wear spectacles? In Step 1 we noted that 2/3 y (boys) wear spectacles. That tells us that 1/3 y (i.e 1/3 boys) do not wear spectacles. Similarly, from Step 1, we learned that 5/6 x (i.e. 5/6 girls) do not wear spectacles.

In this Step 2, the story tells us that these two numbers (boys do not wear spectacles, and girls do not wear spectacles) are equal. In math way, this is to say that 1/3 y = 5/6 x.

Here we go, we now got one equation: 1/3 y = 5/6 x.

Step 3:

In Step 2, we got one equation, however we have 2 symbols or we call 2 variables there. We need one more equation to be able to solve for x and y.

Here, the story tells us “there are 9 more boys than girls in the class”. This piece info gives us a way to build one more equation of x and y. Do you now see how?

When you have 2 equations and 2 variables, you can solve for x and y. Then the total number of students is: x + y.

Hope this is helpful and hope you now can solve it on your own. Let me know if you need more help.

Answer 2

With all these types of problems, define some variables, B for boys and G for girls.

And then write out the equations for each relationship. (You need to read it carefully. For example, (1 - 2/3) is the fraction of boys that do not wear spectacles.)

(1 - 2/3) B = (1 - 1/6) G => 1/3 B = 5/6 G

G + 9 = B

Then use the substitution method to solve the equations. For this method, you need to get one of the variables by itself on one side of an equation. We already have that: G + 9 = B. So,

1/3 (G + 9) = 5/6 G

G = 12

And then plug 12 into either equation to get the other variable: B = 12 + 9 = 21

So there are 33 students in the class.

Answer 3

2/3 B + 1/6 G = 1/3 B + 5/6 G

an equal number wear as don't wear glasses

multiply by 6

4B +G = 2B +5G

2B = 4G

B =2G

B=9+G =2G

G = 9 Girls

B= 18 Boys

2B/3 +G/6 = 2(18)/3 + 9/6 = 13.5

1B/3 +5G/6 = (18)/3+ 5(9)/6) = 6+7.5 = 13.5

total = 27

one girl wears glasses half the time to make this work

if you argue for total =27, with B=15 and G=12

then

2/3 of 15 = 10 boys wearing glasses and 5 don't

and

1/6 of 12 = 2

so 2 girls wear glasses and 10 don't

and

5+10= 15 don't wear glasses

5 boys don't wear glasses, 10 girls don't wear glasses

5+10 = 15 don't wear glasses but 15 doesn't = 10

if you argue for 21 total

then B=9+G

and

21=B+G = 9+G+G

2G = 21-9=12

G= 6, B= 15

but

2/3)(15) + (1/6)6 = 10+1 =11

while

1/3)(15) + 5/6)(6) = 5+5=10

10 doesn't =11

correct answer is 27 total with 18 boys and 9 girls

and one girl wearing glasses half the time to make it work

this can't really be an algebra 1 or 2 question? Your instructor is a tad sadistic

or just maybe there's an error in the problem, miscopied?

schools with common core are trying to make math more difficult with some

problems parents could never solve, and drive students crazy

so, not to discount comments or posts by others, but it's not an easy problem