|
Question 1202710: The ratio of boys to girls among the students who signed up for a basketball competition is 4:3. If 3 boys drop out of the competition and 4 girls join, there will be the same number of boys and girls. Evaluate the number of students who signed up for the basketball competition.
Found 4 solutions by ikleyn, Theo, Edwin McCravy, MathTherapy:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
The ratio of boys to girls among the students who signed up for a basketball competition is 4:3.
If 3 boys drop out of the competition and 4 girls join, there will be the same number
of boys and girls. Evaluate the number of students who signed up for the basketball competition.
~~~~~~~~~~~~~~~~~~~
Initially, 4x boys and 3x girls are signed.
If these numbers change as described, the number of boys will be (4x-3); the number of girls will be (3x+4).
These numbers are equal, so we write this equation
4x - 3 = 3x + 4.
It gives further
4x - 3x = 4 + 3
x = 7.
ANSWER. The number of signed boys is 4*7 = 28; the number of signed girls is 3*7 = 21.
Solved.
--------------------------------
I have read Edwin's notes about my solution, and do not understand clearly,
for what reason he wrote it.
I don't want very much to argue with Edwin.
But he does not leave me any option as to respond.
E d w i n M e
I think Theo's method is better. You may think so - it is your right.
Other people may think differently.
I personally think differently.
It's easier to set up word problems You may think so - it is your right.
when you use more than one unknown. Other people may think differently.
I personally think differently.
Ikleyn always prefers to use one Factually, it is incorrect.
unknown if possible. I may use one approach or another - it is my choice,
and what I choose depends on different circumstances.
Hundreds of my posts at this forum confirm it.
Edwin, it is not a good style to pretend publicly as if you are a Lord and can issue
your undeniable suggestions on every subject. Adult educated people do not make so.
Please do note that it was not me who pushed the stone down the mountain first.
I cordially advise you not to let go of hairpins in my address without necessity.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! b/g = 4/3
(b-3)/(g+4) = 1/1
b = number of boys
g = number of girls
from b/g = 4/3, solve for b to get b = 4/3*g
from (b-3)/(g+4), solve for (b-3) to get b-3 = g+4
add 7 to both sides of this equation to get b = g+7
since they both equal to b, set them equal to each other to get:
4/3*g = g+7
multiply both sides of this equation by 3 to get:
4g = 3g+21
subtract 3g from both sides of this equation to get:
g = 21
since b = 4/3*g, solve for b to get b=4/3*21=28
you have:
b = 28
g = 21
b/g = 28/21 = 4/3
b-3 = 25
g+4 = 25
(b-3)/(g+4) = 25/25 = 1
solution is confirmed to be good.
your solution is:
28 boys and 21 girls signed up for the competition for a total of 49 students.
Answer by Edwin McCravy(20056)  (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
The ratio of boys to girls among the students who signed up for a basketball competition is 4:3. If 3 boys drop out of the competition and 4 girls join, there will be the same number of boys and girls. Evaluate the number of students who signed up for the basketball competition.
Let the multiplicative factor for the number of students who signed up, be x
As the ratio of boys to girls who signed up was 4:3, number of boys who signed up was 4x, and
number of girls, 3x, which makes the total number of students who signed up, 4x + 3x = 7x
With 3 boys dropping out, 4x - 3 remained. And, with 4 girls joining, number of girls became 3x + 4
As the number of boys and girls, then, was the same, then the NEW ratio now equals 1.
We then have: 
4x - 3 = 3x + 4 ----- Cross-multiplying
4x - 3x = 4 + 3
Multiplicative factor for the number of students who signed up, or x = 7
Total number of students who signed up: 7x = 7(7) = 49
|
|
|
| |
