(adsbygoogle = window.adsbygoogle || []).push({}); i need help... it doesnt make sense

1. the ratio of the males to females in a class is 5 to 4. if 5 males and 6 females are taken out, the ratio changes to 4 to 3. how many people are initially there?
27
33
63
81
105

2. a string is cut into 2 pieces that have lengths in ratio 2:9. if one of the string is 42 inches longer then the other one, what is the length of the shorter piece?
6
12
18
24
30

3 a team has won 60$ of the games it has played so far. if the team wins 15 remaining games, it will have won 80% of its season games. how many game will the team play over the entire season.
15
20
25
30
32

Paying 100k for an answer and explanation to the answer....

1. The answer is 81. In an original 5:4 ratio that would mean 45 males and 36 females. When you remove 5 males and 6 females you get 40 males and 30 females. Reduce that ratio and you get 4:3.

2. The shortest piece of string is 12 inches long. If the longer piece is 42 inches longer then the longer piece is 54 inches long. Making the whole string 66 inches long. 2:9 means an 11 piece total ratio, in 66 total inches means 1 piece is equal to 6 inches. 2:9=12:54.

3. 30 games; initially 15 games are played; 60% won means 9 games have been won. If the team wins the next 15, then they have won a total of 24. 24/30 is 80%.

Sorry, I didn't show more work. I just sort of solve these in my head. If you have any questions, I'll do my best to explain.

yeah i mean this was during a practice sat at my afterschool,
you don't have the time to guess and check,
so im trying to get the equations to solve this in the shortest amount of time.

For the 1st questions. It says a 5:4 ratio. So that means 9 total pieces. So the correct original value should be divisible by 9. Then it says removing 5 males and 6 females gives a 4:3 ratio. That's 7 total pieces after removing 11. So your original value must be divisible by 7 after subtracting 11. It has to be divisible by 9 and 7 because we're talking about people and those can't have decimal ratios applied to them because you can't have a decimal person.

For the second question, you have a 2:9 ratio. So that means 11 total pieces. So assume the shorter piece is equal to x. Then (x+(x+42)) must be divisible by 11 because the equation I just put up is for the total length of string. The only number that applies in this case is 12.

For the third question it says the team has won 60% of their games. Then it says if it wins 100% of the next 15 games then the win percentage will be 80%. 100 and 60 balance out to 80 but that's assuming the two percents are based on the same amount of games. Therefore the team must have won 60% of their first 15 games and since they have 15 games left, meaning a total of 30 games in the season.

This is just logic and basic math but most ratio questions can be solved that way; in my experience anyways.

1) A 5:4 ratio means that the number of males divided by the number of females is 5/4. Say there's x boys and y girls. Then x/y=5/4. Then you have some addition info: 5 boys and 6 girls are removed, so the number of boys and girls is now (x-5) and (y-6), and we know the new ratio is 4/3: (x-5)/(y-6)=4/3. Now you have two unknowns (x and y) and two equations, so you can solve for x and y. After a little bit of algebra, you get:

y=4x/5
x=4(y-6)/3+5=4(4x/5-6)/3+5=16x/15-3
x/15=3
x=45
y=4(45)/5=36

So there are 45 boys and 36 girls.


The other two problems are solved in a similar fashion: just setup two equations for the information you're given, then solve for the unknowns.