Q&A - P5 Math

[SAHMwith2boys]

tianzhu:

SAHMwith2boys:

Hi all, encountered the below maths question and need help:


Machine A can produce 450 toys in 5 hours and Machine B can produce 120 less toys in 3 hours. Find the ratio of the number of toys produced by Machine A to the number of toys produced by Machine B every hour.

Would appreciate if explanation and working can be given as well so that I can have a better understanding...thanks a lot... :oops:

Hi

Good Morning.

Machine A

5h ------ 450 toys
1h ------ 90 toys

Machine B

3h ------ 330 toys (450-120)
1h ----- 110 toys

Machine A : Machine B ------ 90:110 ------ 9:11

Best wishes

Thanks TianZhu...

[Jamesbond]

1) Dan spent 2/3 of her money on some gaming accessories. She spent 3/7 of the remaining money on a box of colour pencils and the remaining $24 on a CD game.

a) What fraction of her money was spent on the CD?
b) How much money did Dan have at first?

2) Imu gave 2/7 of his salary to his wife and used 1/3 of his remaining money to pay his bills. Given that he had left $2200 for himself, find the salary of Imu?

Pl explain me in detail. vvv diff…Thanks in advance.

[CRAZYBANANA]

1) Dan spent 2/3 of her money on some gaming accessories. She spent 3/7 of the remaining money on a box of colour pencils and the remaining $24 on a CD game.

a) What fraction of her money was spent on the CD?
$24 = 4/7 of the remaining $
7 unit represents 1/3 of her $
At first, she would have 21 units
Therefore, the fraction is 4/21

b) How much money did Dan have at first?
1 unit = $24/4 = $6
21 unit x $6 = $ 126



2) Imu gave 2/7 of his salary to his wife and used 1/3 of his remaining money to pay his bills. Given that he had left $2200 for himself, find the salary of Imu?
He used 1/3 of 5/7 to pay bills.
He is left with 2/3 x 5/7 = 10/21
1 unit = $2200 / 10 = $220
His salary = 21 x $220 = $4620

[Jamesbond]

thanks a lot

[savoury sweet]

Jamesbond:

1) Dan spent 2/3 of her money on some gaming accessories. She spent 3/7 of the remaining money on a box of colour pencils and the remaining $24 on a CD game.

a) What fraction of her money was spent on the CD?
b) How much money did Dan have at first?

2) Imu gave 2/7 of his salary to his wife and used 1/3 of his remaining money to pay his bills. Given that he had left $2200 for himself, find the salary of Imu?

Pl explain me in detail. vvv diff...Thanks in advance.

HI

As I am still new in this KSparents forum, therefore I have no idea how to post the solution in model method and my scanner is down. So I will try my best in explaining them to you in words instead.

1) Draw 3 units(3/3) in a model. Highlight the last 2 units to indicate spent on gaming accessories also means 2/3 . Therfore you have 1 unit left(1/3).

Bring down the 1/3 model which is the remaining money. Then you have to draw 7 units in that 1/3 model and highlight or shade 3 units (3/7) to indicate the amount spent on a box of color. The remaining 4/7 = $24 is the amount spent on CD games.

The fraction of Dan's money spent on CD is 4/7 x 1/3 = 4/21.


b) 4/7 = $24

----- 4u = 24
----- 1u = 24 / 4 = $6
----- 7u = $6 x 7 = $42

$42 x 3 = $126 is the amount Dan had at first.



2) The method is abt the same, so I just write down the number statement.

7/7 -2/7(given to wife)=5/7 (remaining)
5/7 is also equals to 3/3 as the qns states that Imu used 1/3 to pay bills.

So u have to draw 3 units of model and shade off 1 unit indicating pay bills.

Left with 2 units = $2200
1 units = $1100, so the entire 3units = $3300

the 3 units is also equals to the remaining 5/7 of the main model.
therfore ie 5 units = $3300
1 units = $660, the whole salary of Imu is 7 units---$660 x 7
=$4620


Hope you understand the above.

[bookwormkids]

Q4

Bookmarks are sold at 4 for $5 and pens are sold at 3 for $4. Kenny bought an equal number of bookmarks and pens. He paid a total of $124. How many bookmarks and pens did he buy altogether?

- Any other method to use beside the time consuming guess & check?

Q6
The cost of a pair of soccer boots and a t-shirt is $175. The cost of the t-shirt and a cap is $64. The cost of the pair of soccer boots is 4 times the cost of the cap. How much more does the pair of soccer boots cost than the t-shirt? (Ans sheet: $121. My ans: $111?)

Q7
A pet farm had the same number of kittens, puppies and rabbits at first. After 35 kittens, some puppies and rabbits were sold, there were 65 animals left. There were thrice as many rabbits as puppies left. There were 26 fewer kittens left than the rabbits left. How many rabbits and puppies were sold?

Thank you.

[tianzhu]

bookwormkids:

Q4

Bookmarks are sold at 4 for $5 and pens are sold at 3 for $4. Kenny bought an equal number of bookmarks and pens. He paid a total of $124. How many bookmarks and pens did he buy altogether?

- Any other method to use beside the time consuming guess & check?

Thank you.

Hi

You may use the “Grouping Concept”.

The key point to note is Kenny bought an equal number of bookmarks and pens. Bookmarks are sold in group of 4 and pens sold in group of 3.

For the pens and bookmarks to be equal in numbers, we need to start with a common multiple which is in this case 12 (3 and 4).

4 bookmarks ------ $5
12 bookmarks ------ $15 (3*5)

Likewise

3 pens ------ $4
12 pens ----- $16

Total cost for a group of 12 bookmarks and pens ------- 15+16 ------31

124/31 -------- 4

You’ve 4 groups of 12 bookmarks and pens.

48 bookmarks and 48 pens (96)

Best wishes

[tianzhu]

bookwormkids:

Q6
The cost of a pair of soccer boots and a t-shirt is $175. The cost of the t-shirt and a cap is $64. The cost of the pair of soccer boots is 4 times the cost of the cap. How much more does the pair of soccer boots cost than the t-shirt? (Ans sheet: $121. My ans: $111?)

Thank you.

Hi

121 is the correct answer.

This question touches on simultaneous concept.

Students may use SE if they are familiar with it.

Otherwise, they may solve it pictorially with MD, using letters of the alphabet or labelling as units and parts.

SB + TS ------ 175
C + TS ------ 64

SB ------ CCCC (a pair of soccer boots costs 4 times as much as a cap)

CCCC + TS ------ 175
C + TS ------ 64

CCC ------ 111
C ------ 37

TS ------ 64 – 37 ------27
SB ------ 4*37 ------- 148

148 - 27 ------- 121.

Best wishes

[tianzhu]

bookwormkids:

Q7
A pet farm had the same number of kittens, puppies and rabbits at first. After 35 kittens, some puppies and rabbits were sold, there were 65 animals left. There were thrice as many rabbits as puppies left. There were 26 fewer kittens left than the rabbits left. How many rabbits and puppies were sold?

Thank you.

Hi

You may use MD.

In the end, the number of animals left is:

Rabbits ----- 3 units (3 boxes)
Puppies ----- 1 unit
Kittens ------ 3 units – 26

7 units ------ 65+26 ------91
1 unit ------ 13

Number of rabbits left ------ 3*13 ------ 39
Number of puppies left ------- 13

Number of kittens at first ------ 13+35 ------- 48

Number of rabbits sold ------ 48 – 39 ------ 9
Number of puppies sold ------- 48 – 13 ------ 35

The answer is (35+9) or 44

Best wishes

[bookwormkids]

Hi tianzhu! Thanks so much for your detail explanations!