Out of the original girls and boys at a carnival party 40% of the girls and 10% of the boys left early, 3/4 of them decided to hang out and enjoy the festivities. There were 18 more boys than girls in the party. How many girls were there to begin with?

Question

Out of the original girls and boys at a carnival party 40% of the girls and 10% of the boys left early, 3/4 of them decided to hang out and enjoy the festivities. There were  18 more boys than girls in the party. How many girls were there to begin with?

Gabriel Agustin · Accepted Answer

If I have interpreted this question correctly, it describes an impossible situation.

If #3/4# stayed then #1/4=25%# left early If we represent the original number of girls as #color(red)g# and the original number of boys as #color(blue)b# #color(white)("XXX")40% xxcolor(red) g + 10% xx color(blue)(b) = 25% xx (color(red)g+color(blue)b)# #color(white)("XXX")rarr 40color(red)g+10color(blue)b=25color(red)g+25color(blue)b# #color(white)("XXX")rarr 15color(red)g= 15color(blue)b# #color(white)("XXX")rarr color(red)g=color(blue)b# ...BUT we are told #color(blue)b=color(red)g+18#

Mila Anderson · Answer

undefined Let's denote the number of girls at the beginning of the party as G and the number of boys as B.

Given that 40% of the girls and 10% of the boys left early, we can express the number of girls who left early as 0.4G and the number of boys who left early as 0.1B.

After they left, 3/4 of them decided to hang out, so the number of girls who stayed to enjoy the festivities is 0.6G (since 40% left, 60% stayed) and the number of boys who stayed is 0.9B (since 10% left, 90% stayed).

We're also given that there were 18 more boys than girls in the party. So, we can express this as:

$$B = G + 18$$

Additionally, we know that the total number of girls and boys who stayed to enjoy the festivities is equal to the total number of girls and boys who left early, which can be represented as:

$$0.6G + 0.9B = 0.4G + 0.1B$$

Now, we'll substitute $B = G + 18$ into this equation and solve for G.

$$0.6G + 0.9(G + 18) = 0.4G + 0.1(G + 18)$$

$$0.6G + 0.9G + 16.2 = 0.4G + 0.1G + 1.8$$

$$1.5G + 16.2 = 0.5G + 1.8$$

$$1.5G - 0.5G = 1.8 - 16.2$$

$$1G = -14.4$$

$$G = -14.4/1$$

$$G = -14.4$$

Since the number of girls can't be negative, there may be a mistake in the setup of the problem. It's possible that there's an error in the given information or in the way the problem is formulated.