5/7 students are boys. There are 18 more boys than girls. How many altogther in the group?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Let's denote the number of students as S.

5/7 of them are boys. If we denote the number of boys as B, B = (5/7)*S

The rest of the students are girls. This is equal to (1 - 5/7)*S = (2/7)*S

As the number of boys is 18 more than the number of girls

(5/7)*S = 18 + (2/7)*S

=> (5/7)*S - (2/7)*S = 18

=> (3/7)*S = 18

=> S = 18*(7/3)

=> S = 42

The number of people in the group altogether is 42.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the number of boys be B and the number of girls be G.

There are 18 more boys than girls.

Then, B = G + 18 ...............(1)

Also, given that 5/7 of the students are boys.

==> (5/7)* (B+G) = B............(2)

We will substitute (1) into (2).

==> (5/7) * (G+18 + G) = G+18

==> (5/7) *(2G+18)= G+18

==> Multiply by 7.

==> 10G + 90= 7G + 126

We will combine like terms.

==> 3G = 36

==> G = 12

==> B = 18+12 = 30

==> G + B = 30+12 = 42

Then there are 42 girls and boys in the group.

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