ɪɴ ᴀ ꜱᴄʜᴏᴏʟ 50% ᴏꜰ ᴛʜᴇ ꜱᴛᴜᴅᴇɴᴛꜱ ᴀʀᴇ ʏᴏᴜɴɢᴇʀ ᴛʜᴀɴ 10, 1/20 ᴀʀᴇ 10 ʏᴇᴀʀꜱ ᴏʟᴅ ᴀɴᴅ 1/10 ᴀʀᴇ ᴏʟᴅᴇʀ ᴛʜᴀɴ 10 ʙᴜᴛ ʏᴏᴜɴɢᴇʀ ᴛʜᴀɴ 12, ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ 70 ꜱᴛᴜᴅᴇɴᴛꜱ ᴀʀᴇ 12 ʏᴇᴀʀꜱ ᴏʀ ᴏʟᴅᴇʀ. ʜᴏᴡ ᴍᴀɴʏ ꜱᴛᴜᴅᴇɴᴛꜱ ᴀʀᴇ 10 ʏᴇᴀʀꜱ ᴏʟᴅ?
Answers
SOLUTION
Let us write the fraction for each group of students..
Group A :
Group B : 10 years old: 1/20
Group C : older that 10 but younger than 12: 1/10
Group D : 12 years or older : 70 students
The fraction for group A, B and C together is given by..
, common denominator
, add numerators
The fraction for group D is given by..
and corresponds to 70 students..
If X is the total number of students, then..
7 / 20 of X = 70
or (7 / 20) × X = 70
Solve for X
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to..
Answer:
Let us write the fraction for each group of students..
Group A :
10: 50\% = 50 \sqrt{100 \: } = 1 \sqrt{2}10:50%=50
100
=1
2
\begin{gathered}\\\end{gathered}
Group B : 10 years old: 1/20
\begin{gathered}\\\end{gathered}
Group C : older that 10 but younger than 12: 1/10
\begin{gathered}\\\end{gathered}
Group D : 12 years or older : 70 students
\begin{gathered}\\\end{gathered}
The fraction for group A, B and C together is given by..
\begin{gathered}\\\end{gathered}
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 201/2+1/20+1/10=10/20+1/20+2/20
, common denominator
\begin{gathered}\\\end{gathered}
= 13 / 20 =13/20
, add numerators
\begin{gathered}\\\end{gathered}
The fraction for group D is given by..
\begin{gathered}\\\end{gathered}
20 / 20 - 13 / 20 = 7 / 2020/20−13/20=7/20
and corresponds to 70 students..
\begin{gathered}\\\end{gathered}
If X is the total number of students, then..
7 / 20 of X = 70
or (7 / 20) × X = 70
Solve for X
X = 70 × (20 / 7) = 200X=70×(20/7)=200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to..
(1 / 20) \: of \: 200 = 10 \: students(1/20)of200=10students