Problem Solving

S

smer

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Mar 5, 2022
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Good day,
Can you help out in this please?

The Balloon Man has some balloons to give to the children at a birthday party.
If he gives 4 balloons to each child, he will have 35 balloons left over.
If he gives 6 balloons to each child, he will have 11 balloons left over.
How many children are there are the party?
 

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This being in the arithmetic section, it can not be done using algebra. I can only think of using the trial and error method.
Hint: start with assuming there are 10 children at the party.
 
Using algebra (because sometimes problems get put in the wrong section):

Let b be the number of balloons and c be the number of children.

"
If he gives 4 balloons to each child, he will have 35 balloons left over."
b- 4c= 35 so b= 4c+ 35.

"If he gives 6 balloons to each child, he will have 11 balloons left over."
b- 5c= 11 so b= 5c+ 11.

Solve b= 4c+ 35= 5c+ 11 for c.
 
smer said:
Good day,
Can you help out in this please?

The Balloon Man has some balloons to give to the children at a birthday party.
If he gives 4 balloons to each child, he will have 35 balloons left over.
If he gives 6 balloons to each child, he will have 11 balloons left over.
How many children are there are the party?
Click to expand...
Smer has not visited the site after 030522.
 
Good idea. But this was the second time today I was criticized for responding to an old post- and this one wasn't very old!
 
Subhotosh Khan said:
Shiloh said:
Sigh. I am getting tired of saying this: the original poster isn't the only one who can learn from a response!
Click to expand...
That was NOT meant as criticism of your work.......
Click to expand...

Perhaps you should have criticized Shiloh's work (instead of 'Liking' it, lol) because it is wrong!

Solving his equations (4c+35=5c+11) for c produces 24 as the number of children present but substituting that value back into the original statements produces two different answers for the number of balloons available! This puzzled me for quite some time (because the algebra appeared to be sound, even if not "warranted", lol) until I spotted his mistake.

Alternatively, the iterative method suggested by Steven G very quickly produces the correct number of children present as 12, which then swiftly led me to discovering where Shiloh had boobed, :eek:

His second equation: b-5c=11 should, of course, have been b-6c=11, thus giving the equivalence of 4c+35=6c+11 and thence c=12!

I suppose the best thing that we can learn (even if the OP doesn't benefit) from Shiloh's response is that we all make mistakes. :D:unsure::giggle:
 
The Highlander said:
Perhaps you should have criticized Shiloh's work (instead of 'Liking' it, lol) because it is wrong!

Solving his equations (4c+35=5c+11) for c produces 24 as the number of children present but substituting that value back into the original statements produces two different answers for the number of balloons available! This puzzled me for quite some time (because the algebra appeared to be sound, even if not "warranted", lol) until I spotted his mistake.

Alternatively, the iterative method suggested by Steven G very quickly produces the correct number of children present as 12, which then swiftly led me to discovering where Shiloh had boobed, :eek:

His second equation: b-5c=11 should, of course, have been b-6c=11, thus giving the equivalence of 4c+35=6c+11 and thence c=12!

I suppose the best thing that we can learn (even if the OP doesn't benefit) from Shiloh's response is that we all make mistakes. :D:unsure::giggle:
Click to expand...
I made the cardinal mistake of staring at the screen instead of putting pencil to paper and glossed over the mistake (more over I did not check back with the original equation). Sad part is I complain about these all the time . Sheesh...
 
Subhotosh Khan said:
I made the cardinal mistake of staring at the screen instead of putting pencil to paper and glossed over the mistake (more over I did not check back with the original equation). Sad part is I complain about these all the time . Sheesh...
Click to expand...
First, let the total no. of balloons be BT and no. of children be C. So, that gives us two equations to be solved:
BT-4C=35
BT-6C=11
By solving the above equations give C=12 and BT=83.

Hopefully my above solution helps. Thanks :)
 
According to question
let no of ballons be x and no of students be y,
so,
x-4y=35
x-6y=11

after solving these equations you will get y=12
so there are 12 students in class.
 
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