Tutor MathsGuru: Ask me for your burning Maths questions!

[mathsguru]

YLH88:

Hi Mathsguru,


Need to trouble you again with the below 2 questions.

1) Shop X sells a table lamp for $300 which is 25% less than the price which Shop Y sells it for.

a) What is the price of the table lamp in Shop Y ?

b) During a sale, both shops offer an equal percentage discount on the table lamp. Mr Song buys the table lamp in Shop X and pays $85 less than the discounted price in Shop Y. What is the percentage discount ?

For part (a), I got the answer is $400, is it correct ?
For part (b), i lost liao ...

2) The figure attached, not drawn to scale, is make up of two overlapping rectanlges, A and B. The ratio of the area of Rectangle A to that of Rectangle B is 2:5. If 25% of Rectangle A is shaded, what fraction of the figure is unshaded ?
I tried working out and got the answer as 25%/550%, is it correct ?

http://www.postimage.org/image.php?v=PqlAxYJ

Thank you so much!!

Hi YLH88,

Here're my solutions and explanations.


MathsGuru

http://www.postimage.org/image.php?v=aVbr_Bi

http://www.postimage.org/image.php?v=aVbrY69

[mathsguru]

OngMum:

Hi Mathsguru, I have a couple of questions here need your assistance in terms of model drawing. Thank you in advance for your help.


1. Lena and Salimah shared some beads. If Lena gives Salimah 1/2 of her beads, Salimah will have 95 more beads than Lena. If Lena gives Salimah 1/6 of her beads, she will have 15 beads fewer than Salimah.
a. How many beads do the two girls have altogether?
b. If both girls combined their beads and packed them into bags of beads, how many complete bags of 25 beads would they have?

2. There were 310 adults in a hall. When 25% of the men left the hall, and 40 women came in. There was equal number of men and women. How many women were there at first?

3. Samuel gets $5 more pocket money than Barbara each week. They each spend $15 per week and save the rest. When Samuel saves $80, Barbara only saves $40. How much pocket money does Samuel get each week?

4. On a farm, there are 1/5 as many hens as goats and twice as many cows as hens. If the total number of legs of the three kinds of animals is 600. How many cows are there on the farm?

Cheers!

Hi OngMum,

Here are my solutions and explanations. Hope they help!


MathsGuru

http://www.postimage.org/image.php?v=TsCuO_9

http://www.postimage.org/image.php?v=TsCuRui

http://www.postimage.org/image.php?v=TsCuTZr

http://www.postimage.org/image.php?v=TsCuMv0

[persistent]

1. Lena and Salimah shared some beads. If Lena gives Salimah 1/2 of her beads, Salimah will have 95 more beads than Lena. If Lena gives Salimah 1/6 of her beads, she will have 15 beads fewer than Salimah.

a. How many beads do the two girls have altogether?
b. If both girls combined their beads and packed them into bags of beads, how many complete bags of 25 beads would they have?

Scenario 1
…Lena…Salimah
Before…12 units…95
…-6 units…+6 units
…
After…6 units…6 units+95
…

Scenario 2
…Lena…Salimah
Before…12 units…95
…-2 units…+2 units
…
After…10 units…2 units+95
…

10 units = 2 units + 95 - 15
10 units = 2 units + 80
8 units = 80
1 unit = 10

Ans.
(a) 12 x 10 + 95 = 215
(b) 215 / 25 = 8 bags



2. There were 310 adults in a hall. When 25% of the men left the hall, and 40 women came in. There was equal number of men and women. How many women were there at first?


…Men…Women
Before…4 units…3 units - 40
…-1 unit…+40
…
After…3 units…3 units
…

4 units + 3 units - 40 = 310
7 units - 40 = 310
7 units = 40 + 310 = 350
1 unit = 50

Ans. At first, women = 3 x 50 - 40 = 110



3. Samuel gets $5 more pocket money than Barbara each week. They each spend $15 per week and save the rest. When Samuel saves $80, Barbara only saves $40. How much pocket money does Samuel get each week?

Total difference = $80-$40 = $40
Individual diff = $5
No. of weeks = 40/5 = 8 weeks

Samuels takes 8 weeks to save $80. He saves $10 each week.

…Samuel
Spending…$15
Savings…$10
…
Pocket Money…$25
…



4. On a farm, there are 1/5 as many hens as goats and twice as many cows as hens. If the total number of legs of the three kinds of animals is 600. How many cows are there on the farm?

…Hens…Goats…Cows
No. of animals…1 unit…:…5 units…:…2 units
…x 2 legs…x 4 legs…x 4 legs
…
Total legs…2 units…20 units…8 units
…

2 units+20 units+ 8 units = 30 units = 600
…1 unit = 20

Ans. No. of cows = 2 x 20 = 40

[Dharma]

YLH88:

[quote]Q2

Ratio of Rect A: Rect B = 2 : 5 = 4 : 10

Ratio of Rect A (Shaded) : Ratio of Rect A (Unshaded) = 1 : 3

Ratio of A (Unshaded) : Ratio of A & B (Shaded) : Ratio of B (Unshaded) = 3 : 1 : (10-1) = 3:1:9

Fraction of figure that is unshaded = 12/13

Hi Dharma,

Thank you for the solution. For Q2, how come we need to change the ratio of rect A : rect B = 4:10 instead of using 2:5 ?[/quote]Hi YLH88

The reason is … qn says 25% (1/4) of Rectangle A is shaded.

For Rectangle A, ¼ is shaded and ¾ is unshaded. Ratio of shaded area of Rect A : Area of Rect A = 1 : 4

If Area of Rect A consist of 4 parts, then Area of Rect B must be 10 parts … given that ratio of Rect A : Rect B = 2: 5 = 2 x2 : 5x2 = 4:10

[YLH88]

Hi Mathsguru, Dharma,


Thank you very much for the solution and explanation. Now I can explain to my DS

Regards

[Hifive]

Hi Mathsguru


Need your help in this question:

A group of people met a party. Each person shook hands with everyone else. Mr Li shook hands with 3 times as many men as women. Mrs Li shook hands 4 times as many men as women. How many men and how many women were there at the party?

Thanks in advance!

[CoffeeCat]

Hifive:

Hi Mathsguru


Need your help in this question:

A group of people met a party. Each person shook hands with everyone else. Mr Li shook hands with 3 times as many men as women. Mrs Li shook hands 4 times as many men as women. How many men and how many women were there at the party?

Thanks in advance!

I am not mathsguru but...
Lets say there are x number of women at the party.
Mr Li will shook hands with 3x number of men, and x number of women.
His wife will shook hands with (3x+1) number of men (including her husband)
and (x-1) other women.
3x+1 = 4(x-1) x =5

If you are interested in model form you should wait for mathsguru's ans.
However drawing of model is similar by substituting 1 unit for x.

[OngMum]

Hi Mathsguru & Sister,


Thank you so much for the solution with explanation.

Cheers!

[mathsguru]

Hifive:

A group of people met a party. Each person shook hands with everyone else. Mr Li shook hands with 3 times as many men as women. Mrs Li shook hands 4 times as many men as women. How many men and how many women were there at the party?

Hi Hifive,

Here's my solution. Saw the same question before in a book and there's a shortcut to it. However, I think the shortcut works only if the question is of the exact same nature (you can try with other no.s like 6 or 7 times, then no. of women = 8). In my opinion, I won't really encourage my students to \"memorise\" such solutions cos they become non-thinking students and may have difficulty applying concepts in actual tests/exams. Hence, it's safer to go by model method...

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=TsEKQ9A

[Hifive]

Hi CoffeeCat


Thanks for your explanation.


Hi mathsguru

Thanks for your model and explanation.

Cheers.