# arithmetic problem

• Apr 13th 2010, 08:46 AM
sri340
arithmetic problem
In a class room which has 30 students, 16 of the students are boys , 23 are ten years old and 6 are girls who are not 10 years old. How many students in the class are ten-year old boys ?

A 8 b 10 c 12 d 15 e 16
• Apr 13th 2010, 09:32 AM
Quote:

Originally Posted by sri340
In a class room which has 30 students, 16 of the students are boys , 23 are ten years old and 6 are girls who are not 10 years old. How many students in the class are ten-year old boys ?

A 8 b 10 c 12 d 15 e 16

If there are 23 ten year olds there are 30-23 = 7 students who are NOT 10.

6 of these are girls so that means 1 must be a boy.

Since there are boys in the class and one of them is not 10, we know there are 16-1 = 15 10 year old boys in the class.
• Apr 13th 2010, 11:09 AM
AliceFisher
We know the size of the class is 30 and that there are 16 boys in that class.

1. There are therefore 14 girls in the class.

We know that 6 of the girls in the class are under 10

2. There are therefore 8 girls who are over 10.

We know that 23 of the students in the class are over 10.

3. So if we deduct the girls from this total everyone left will be...
• Apr 13th 2010, 11:10 AM
AliceFisher
Though I do rather like Deadstars more direct solution :)
• Apr 13th 2010, 07:25 PM
Soroban
Hello, sri340!

Quote:

In a class room which has 30 students, 16 of the students are boys,
23 are ten years old, and 6 are girls who are not 10 years old.
How many students in the class are ten-year old boys?

. . (a) 8 . . (b) 10 . . (c} 12 . . (d) 15 . . (e) 16

Place the given data in a chart . . .

. . $\begin{array}{c||c|c||c}
& \text{age 10} & \text{not 10} & \text{total} \\ \hline \hline
\text{Boys} & & & 16 \\ \hline \text{Girls} & & 6 & \\ \hline \hline
\text{Total} & 23 & & 30 \end{array}$

You should be able to complete the chart:

. . $\begin{array}{c||c|c||c}
& \text{age 10} & \text{not 10} & \text{total} \\ \hline \hline
\text{Boys} & {\color{red}15} & {\color{red}1} & 16 \\ \hline \text{Girls} & {\color{red}8} & 6 & {\color{red}14} \\ \hline \hline
\text{Total} & 23 & {\color{red}7} & 30 \end{array}$