# ratio to ratio club membership

#### karush

##### Well-known member
60% of the members of our club are men and the rest were women. When 45 new members joined the club, the number of a female members increased by 50% and the number of men was 1 1/2 times as many as before. how many club members were there initially?

ok from the $\dfrac{60\%}{40\%}$ ration we have $\dfrac{3}{2}=\dfrac{m}{w}$

by changing the ratio $\dfrac{3+1.5(3)}{2+1}=\dfrac{15}{6}=\dfrac{5}{2}=\dfrac{m}{w}$

$\dfrac{m}{m-45}=\dfrac{5}{2}\quad m=75$

howeve when I tried to appy this it didn't jive

thot this would be slam dung but   #### skeeter

##### Well-known member
MHB Math Helper
The statements, “increased by 50%“ and “1.5 times as many as before” say the same thing, so the final ratio is unchanged from the 3/2 initial ratio. The ratio of m/w in the 45 that join is also 3/2.

Of the 45 new members, 27 are men and 18 are women

therefore, there were initially 54 men and 36 women

54+27 = 1.5(54)

36+18 = 1.5(36)

• karush

#### Country Boy

##### Well-known member
MHB Math Helper
60% of the members of our club are men and the rest were women. When 45 new members joined the club, the number of a female members increased by 50% and the number of men was 1 1/2 times as many as before. how many club members were there initially?

ok from the $\dfrac{60\%}{40\%}$ ration we have $\dfrac{3}{2}=\dfrac{m}{w}$

by changing the ratio $\dfrac{3+1.5(3)}{2+1}=\dfrac{15}{6}=\dfrac{5}{2}=\dfrac{m}{w}$

$\dfrac{m}{m-45}=\dfrac{5}{2}\quad m=75$

howeve when I tried to appy this it didn't jive

thot this would be slam dung but   I hope you mean "slam dunk"!

Let N be the number of members
"60% of the members of our club are men and the rest were women."
So there are .6N men and .4N women in the club.

"When 45 new members joined the club, the number of a female members increased by 50% and the number of men was 1 1/2 times as many as before."

As you have been told "increased by 50%" and and "1 1/2 times as many" are the same thing. There were .6N men and 50% of that is .3N so now there are .6N+ .3N= .9N men. There were .4N women and1/2 of that is .2N so now there are .6N women. There were 45 new member so now there are a total of N+ 45 members.

So .9N+ .6N= 1.5N= N+ 45.

Subtracting N from both sides .5N= 45. Dividing by .5 (the same as multiplying both sides by 2) N= 90.

There were, originally, 90 members.

Check: There were 90 members and 60% of them were men so there were 54 men. 40% of the members are women so there were 36 women. Half of 54 is 27 and half of 36 is 18. So the number of men increased by 27 to 54+ 27= 81 and the number of women increased by 18 to 36+ 18= 54. There are now 81+ 54= 135 members. Yes, 135- 90= 45 new members.

• karush