Q&A - PSLE Math
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Chan09:
HiI 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
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. -
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
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hazelwong:
HiHi, 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
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. -
MathIzzzFun:
Ahhh... tha's so much easier than the proposed method. Looks like sometimes some books are not so good, despite all their claims!
Hihazelwong:
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
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.
Thanks so much!
:thankyou: -
MathIzzzFun:
I'm afraid I don't get this:
HiChan09:
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
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.
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 ? -
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 ! -
mathnoobs:
I'm afraid I don't get this:
HiMathIzzzFun:
[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
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.
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. -
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 -
Hi anneshirleygilbert,
Your answer is correct.
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anneshirleygilbert:
HiHi 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
yes, your answers are right. I started the solution from the end stage. You could start from the front of the question ie
Charlie --> 7u + 490,
Charlie spent --> 1u + 70,
Eugene spent --> 1u + 50, so
Eugene's money --> 5u + 250 = 7u
1u --> 125
cheers.
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