Ratio

[leonswati]

After one fifth of the adults at a party left the ratio of the adult to teens was 2:3. Later when 44 teens left the ratio of adult to teen was 5:2. How many people were still at the party after the teens left?

I dont have the answer choices but I would appreciate if someone can help.. A little confused..

[GMATGuruNY]

After one fifth of the adults at a party left the ratio of the adult to teens was 2:3. Later when 44 teens left the ratio of adult to teen was 5:2. How many people were still at the party after the teens left?

I dont have the answer choices but I would appreciate if someone can help.. A little confused..

Write equations with respect to the number of ADULTS, which is the same in each ratio.

After the teens leave:
Let x = the total number of people.
a:t = 5:2.
Thus, of every 7 people, 5 are adults and 7 are teens, implying that the adults are 5/7 of the total:
a = (5/7)x.

Before the 44 teens leave:
The total number of people = x+44.
a:t = 2:3.
Thus, of every 5 people, 2 are adults and 3 are teens, implying that the adults are 2/5 of the total:
a = (2/5)(x+44).

Since the number of adults is the same in each ratio:
(5/7)x = (2/5)(x+44)
25x = 14x + 616
11x = 616
x = 56.

[aneesh.kg]

Let the number of adults to teens be A and T respectively.
When 1/5th of the adults left number of Adults at the party become (4A/5),
(4A/5)/T = 2/3
6A = 5T --(1)

After this, 44 Teens leave,
(4A/5)/(T - 44) = 5/2
or
1.6A = 5T - 220 --(2)
Substituting the value of 5T from equation (1) in (2),
1.6A = 6A - 220
OR A = 50, T =6*50/5 = 60
Since 44 of them left, 16 Teens remain. Number of Adults remaining = (4/5)*(50)
Total number of people now = 40 + 16 = 56