Q&A - PSLE Math

[Chan09]

I do need help as I can solve using algebra but even looking at models this is tough:

a group of friends play tennis. each of them play with everyone else. Ann played with 4 times as many girls as boys. Bob played with 5 times as many girls as boys.
a) how many people were there altogether? ans: 31 people
b) were there more boys than girls and how many more? ans: 19 more girls than boys

[MathIzzzFun]

Chan09:

I do need help as I can solve using algebra but even looking at models this is tough:

a group of friends play tennis. each of them play with everyone else. Ann played with 4 times as many girls as boys. Bob played with 5 times as many girls as boys.
a) how many people were there altogether? ans: 31 people
b) were there more boys than girls and how many more? ans: 19 more girls than boys

Hi

Ann played with 4 times as many girls as boys, so
Girls : Boys --> 4u +1 : 1u,
total 5u + 1 people and there were 3u + 1 more girls

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

cross multiply or equalize --> 4u + 1 = 5u -5
1u --> 6
5u + 1 = 31
3u+1 --> 19

There were 31 people and there were 19 more girls than boys.

cheers.

[hazelwong]

Hi, I came across this type of question:

Charlie had $490 more than Eugene. Charlie spent 1/7 of his money, Eugene spent 1/5 of his money. If Eugene spent $20 less than Charlie, find the total amount of money the children had in the end.
The answer given is such a complex model (subdivided into many units) :? that I wonder if there is an easier way?
TIA

[MathIzzzFun]

hazelwong:

Hi, I came across this type of question:

Charlie had $490 more than Eugene. Charlie spent 1/7 of his money, Eugene spent 1/5 of his money. If Eugene spent $20 less than Charlie, find the total amount of money the children had in the end.
The answer given is such a complex model (subdivided into many units) :? that I wonder if there is an easier way?
TIA

Hi

Eugene's money --> 5 units
Eugene spent --> 1 unit
Charlie spent --> 1 unit + 20
Charlie's money --> 7 x (1 unit + 20) = 7 units + 140
So, 7 units + 140 = 5 units + 490
1 unit --> 175
...you should be able to complete the solution from here

cheers.

[hazelwong]

MathIzzzFun:

hazelwong:

Hi, I came across this type of question:

Charlie had $490 more than Eugene. Charlie spent 1/7 of his money, Eugene spent 1/5 of his money. If Eugene spent $20 less than Charlie, find the total amount of money the children had in the end.
The answer given is such a complex model (subdivided into many units) :? that I wonder if there is an easier way?
TIA

Hi

Eugene's money --> 5 units
Eugene spent --> 1 unit
Charlie spent --> 1 unit + 20
Charlie's money --> 7 x (1 unit + 20) = 7 units + 140
So, 7 units + 140 = 5 units + 490
1 unit --> 175
...you should be able to complete the solution from here

cheers.

Ahhh... tha's so much easier than the proposed method. Looks like sometimes some books are not so good, despite all their claims!
Thanks so much!
:thankyou:

[mathnoobs]

MathIzzzFun:

Chan09:

I do need help as I can solve using algebra but even looking at models this is tough:

a group of friends play tennis. each of them play with everyone else. Ann played with 4 times as many girls as boys. Bob played with 5 times as many girls as boys.
a) how many people were there altogether? ans: 31 people
b) were there more boys than girls and how many more? ans: 19 more girls than boys

Hi

Ann played with 4 times as many girls as boys, so
Girls : Boys --> 4u +1 : 1u,
total 5u + 1 people and there were 3u + 1 more girls

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

cross multiply or equalize --> 4u + 1 = 5u -5
1u --> 6
5u + 1 = 31
3u+1 --> 19

There were 31 people and there were 19 more girls than boys.

cheers.

I'm afraid I don't get this:

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

why is Boys = 1u-1 ? and Girls = 4u+1 ? is that from the previous statement ?

[2DMommy]

Please help with this question :


After a maths quiz, Mr Li gave the 3 prize winners a box of pencils to share. The 1st winner received 2/3 of the pencils plus 1/3 of a pencil. The 2nd winner received 2/3 of the remainder plus 1/3 of a pencil. The 3rd winner received 2/3 of the new remainder plus 1/3 of a pencil, but there were no pencils left after this. How many pencils were there in all ?

thanks !

[MathIzzzFun]

mathnoobs:

MathIzzzFun:

[quote=\"Chan09\"]I do need help as I can solve using algebra but even looking at models this is tough:

a group of friends play tennis. each of them play with everyone else. Ann played with 4 times as many girls as boys. Bob played with 5 times as many girls as boys.
a) how many people were there altogether? ans: 31 people
b) were there more boys than girls and how many more? ans: 19 more girls than boys

Hi

Ann played with 4 times as many girls as boys, so
Girls : Boys --> 4u +1 : 1u,
total 5u + 1 people and there were 3u + 1 more girls

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

cross multiply or equalize --> 4u + 1 = 5u -5
1u --> 6
5u + 1 = 31
3u+1 --> 19

There were 31 people and there were 19 more girls than boys.

cheers.

I'm afraid I don't get this:

Bob played with 5 times as many girls as boys,
Girls : Boys --> 4u + 1 : 1u -1 = 5 : 1

why is Boys = 1u-1 ? and Girls = 4u+1 ? is that from the previous statement ?[/quote]Hi

Ann played with 4 times as many girls as boys, so if she played with 1 unit of boys, she played with 4 units of girls. So, total number of girls = 4 units + 1 (Ann)

So, Bob will play with 1 unit - 1 (Bob) of boys and 4 units + 1 of girls.

cheers.

[anneshirleygilbert]

Hi MathIzzzFun,


Charlie had $490 more than Eugene. Charlie spent 1/7 of his money, Eugene spent 1/5 of his money. If Eugene spent $20 less than Charlie, find the total amount of money the children had in the end.


Eugene’s money –> 5 units
Eugene spent –> 1 unit
Charlie spent –> 1 unit + 20
Charlie’s money –> 7 x (1 unit + 20) = 7 units + 140
So, 7 units + 140 = 5 units + 490
1 unit –> 175
…you should be able to complete the solution from here

I’m a little confused. Should what Charlie spent have been 1u + 70?
seeing he spent (1/7 of 7 units and 1/7 of $490)?
We did this question using simultaneous equations and our answers are $1170 for Charlie and $700 for Eugene. Are our answers correct?

TIA

[small]

Hi anneshirleygilbert,


Your answer is correct.