4/9of a group of students are girls .if there are 17more boys than girls ,how many students are there altogether
To find the total number of students, we need to determine the number of boys and girls in the group. Let's break down the problem step by step:
Step 1: Let's assume the total number of students in the group as 'x.'
Step 2: Since 4/9 of the students are girls, we can find the number of girls by multiplying 'x' by 4/9:
Number of girls = (4/9) * x
Step 3: We are given that there are 17 more boys than girls. So, we can calculate the number of boys by adding 17 to the number of girls:
Number of boys = Number of girls + 17
Step 4: Now, we can find the total number of students by adding the number of boys and girls together:
Total number of students = Number of girls + Number of boys
Combining steps 2, 3, and 4, we have:
Total number of students = (4/9) * x + ( (4/9) * x + 17 )
Simplifying further:
Total number of students = (8/9) * x + 17
Therefore, the total number of students is given by the expression (8/9) * x + 17.
S = number of students
g = number of girls
b = number of boys
b = g + 17
S = g + b
S = g + g + 17
S = 2 g + 17
g = 4 / 9 S so :
S = 2 * ( 4 / 9 ) S + 17
S = ( 8 / 9 ) S + 17 Subtract ( 8 / 9 ) S to both sides
S - ( 8 / 9 ) S = ( 8 / 9 ) S + 17 - ( 8 / 9 ) S
( 9 / 9 ) S - ( 8 / 9 ) S = 17
( 1 / 9 ) S = 17 Multiply both sides by 9
S = 153
Proof :
g = ( 4 / 9 ) * 153 = 4 * 153 / 9 = 612 / 9 = 68
b = S - g = 153 - 68 = 85
b - g = 85 - 68 = 17