# Ratio / Percentage: Number leaving so 98% of returnees are

#### ryank

##### New member
Could anyone help me with this?

How many girls would have to leave a room in which there are 99 girls and 1 boy in order that 98% of the remaining persons would be girls?

Equation?

This is what I have but I think it's wrong: .98(99) = 97.02 one would have to leave.

Thanks
Ryan

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: Ratio / Percentage word problem

ryank said:
Could anyone help me with this?

How many girls would have to leave a room in which there are 99 girls and 1 boy in order that 98% of the remaining persons would be girls?

Equation?

This is what I have but I think it's wrong:
.98(99) = 97.02 one would have to leave.

Thanks
Ryan
What is the % of girls to start with?

Suppose 'g' number of girls leave the room.

How many girls are in the room (now)?

How many total persons are in the room (now)?

What is the % of girls in the room (now)? .........................(1)

Equate (1) to 98% and solve for 'g'.

#### Mrspi

##### Senior Member
Re: Ratio / Percentage word problem

ryank said:
Could anyone help me with this?

How many girls would have to leave a room in which there are 99 girls and 1 boy in order that 98% of the remaining persons would be girls?

Equation?

This is what I have but I think it's wrong:
.98(99) = 97.02 one would have to leave.

Thanks
Ryan
I'd start by "naming things".

You're looking for the number of girls who need to leave

Let x = number of girls who leave

There were 99 girls to begin with. If x of them leave, how many girls will be left?

There were 100 people to begin with. If x of them leave, how many people will be left?

You want the ratio of girls to people there to be 98%....

number of girls / number of people = 98/100

See what you can do with that....

#### Denis

##### Senior Member
Re: Ratio / Percentage word problem

Hint: what's half of 98? Or: 98 + 2 = 100

#### Subhotosh Khan

##### Super Moderator
Staff member
This problem made me check my problem-solution twice - by giving a counter-intuitive answer.

The begining percentage is 99%.

The final percentage is 98% - I expected the answer should may be 1 or 2 girls leaving (initial and final conditions being so "near" each other).

When the answer came back that more than half the girls (50) would have to leave - it made re-check my work - then my thought process (what did I not consider to expect such a wrong magnitude of answer). Then I realized the final and initial conditions were quite differnt from the boy's perspective (lucky him). The percentage of male in the room "doubled" - quite different from the initial condition.