Question

20 girls left, now there are 2 boys for each girl. Then 20 of the boys left too. There were now 3 times as many girls as boys. how many boys and girls were at the beginning of theparty?

Answer 1

Let x and y be the number of boys and girls at the beginning of the party.

From ''20 girls left, now there are 2 boys for each girl.'', that means the number of boy is twice of that of girls.
Number of girls left = y - 20 (since 20 of them left)

number of boy is twice of that of girls
=> number of boys = 2 x number of girls
=> x = 2 (y-20) ----(1)

From ''Then 20 of the boys left too. There were now 3 times as many girls as boys. ''
Number of boys left = x-20

There were now 3 times as many girls as boys.
=> Number of girls = 3 x number of boys
=> (y-20) = 3 (x-20) ---(2)


Now, solve equation (1) and (2).

Answer 2

there were 40 boys and 33 girls at he beginning of the part???? still dont understand!!!

Answer 3

can someone help?

Answer 4

That's not the answer I've got...
Which part you don't understand?

Answer 5

for the first equation i get 20=y Does it means that there were 20 girls left after 20 were gone? therefore there were 40 girls at the beginning of the party/

Answer 6

is it right?

Answer 7

Nope, it doesn't seem right!
How do you get 20=y from the first equation?

Answer 8

x=2(y-20)
x=2y-40
40x=2y all divided by 2
20x=y

Answer 9

For the step :40x=2y all divided by 2, it is not right.

x=2y-40
You can only add 40 to both sides, then divide both sides by two to make y as the subject. But you don't have to do so actually.

Answer 10

It is a equation in two unknowns, so, basically, you cannot solve it alone.

Answer 11

so for equatin one this is all th eunswer: x=2y-40?

Answer 12

for equatin 2 i have: y-20=3x-60

Answer 13

Yup! Now, you need to solve these two equations. Do you know how to solve it?

Answer 14

no

Answer 15

Have you learnt how to solve simultaneous questions yet?

Answer 16

if i did it was looong time ago. this should be easy my class is called: foundations of math x teaching. so, i guess anyone should be able to solve this. but no me...( its hard x me

Answer 17

Hmm.. For this question. You get two question so far. First one x= 2y-40, the second one, y-20 = 3x-60. You can use the method of substitution to solve it. That is substituting equation one into two. I meant replace x by 2y-40 in the second equation so that the equation would be in one variable and you can solve y.

Answer 18

The ratio of boys to girls after 20 girls left is:\[\frac{B}{G-20}=2\]The ratio of girls to boys after an additional 20 girls left is:\[\frac{G-20}{B-20}\text{= }3\]Solve the above equations for B and G.\[\{B=24,G=32\} \]

Answer 19

is it: y=6y-180+20
y=6y-60
divided by 6
y=negative 10.....is no right..i know. what is it?

Answer 20

The first step is wrong.
Remember the second equation is
y - 20 = 3x - 60
Sub. x= 2y-40 into the above equation:
y - 20 = 3 ( 2y-40 ) - 60 <- this is the right one.

Answer 21

My bad.

"The ratio of girls to boys after an additional 20 girls left is:"

should have been written:

"The ratio of girls to boys after an additional 20 boys left is:"

Answer 22

to Callisto: yes i did that but then i did this: y-20=3(2y-40)-60
y-20=6y-120-60

Answer 23

to callisto; IS IT; y-20=(6y-120)-60

Answer 24

32 girls take away 20 girls is 12 girls compared to 24 boys; there are now twice as many boys as girls.

24 boys take away 20 boys leaves 4 boys compared to 12 girls; there are now three times as many girls as boys.

Answer 25

Yup, you're on the right track!

Answer 26

So, do the additions/subtractions for like terms. Isolate y also to solve y.

Answer 27

y-20=(6y-120)-60
plese help on this whats the nxt step..

Answer 28

y-20=(6y-120)-60
y-20=6y-120-60
Add 20 to both sides
y-20 + 20 =6y-120-60 + 20
What do you get?

Answer 29

y=6y-160

Answer 30

Then, subtract both sides by 6y, what do you get?

Answer 31

y=154

Answer 32

Why?

Answer 33

y=6y-180+20...now subtract both sides by 6
y-6=-160
y=154

Answer 34

Subtract both sides by 6 doesn't help you cancel 6y. You need to subtract 6y from both sides.

Answer 35

y=-160? please ......tell me more i need to resolve it x my class is in 20 minutes.

Answer 36

y=6y-180+20
subtract both sides by 6y
y - 6y=6y-180+20 - 6y
What do you get after simplifying it?

Answer 37

y=32

Answer 38

5y=-160
then i divided all by 5
then i got y=-32 but i know it can b a neg. number. ist right -32?

Answer 39

-32 is not right.
You made a mistake in your first step.
y-6y = -5y, not 5y

Answer 40

That's the reason why you get a negative value for y.

Answer 41

i got it now! thank u very very much x all ur patience with me . i would try to resolve the rest!

Answer 42

You're welcome :) Tell me if you have any problems for this question, I would try to help if I can :)

Answer 43

answer: 32 girls and 24 boys at beginning of party. is it right?

Answer 44

Yes. Refer to my post, 24 posts back.