Q&A - PSLE Math

[MathWithModels]

Question:

Eunice, Grace and Joyce collect badges as their hobby. At first,
Eunice gave 2/5 of her badges to Grace. Grace then gave 3/8 of what
she had to Joyce. Then Joyce gave 1/6 of what she had to Eunice. In
the end, they had 150 badges each. How many badges did Eunice
have at first?



Answer:

We work backwards, beginning with each of them having 150 badges in the end.

In the end:

Eunice: 150
Grace: 150
Joyce: 150

Last transfer: Joyce gave 1/6 of what she had to Eunice.

Joyce had 150 after she gave 1/6 of her badges to Eunice.
So 150 is 5/6 of her badges. She had 150 * 6 / 5 = 180 badges before, and gave 30 to Eunice.
Before Joyce gave her badges to Eunice, the girls had

Eunice: 150 - 30 = 120 (she had 30 fewer badges before)
Grace: 150 (unchanged)
Joyce: 150 + 30 = 180 (she had 30 more badges before)

Second last transfer: Grace gave 3/8 of what she had to Joyce.

Grace had 150 after she gave 3/8 of her badges to Joyce.
So 150 is 5/8 of her badges. She had 150 * 8 / 5 = 240 badges before, and gave 90 to Joyce.
Before Grace gave some of her badges to Joyce, the girls had

Eunice: 120 (unchanged)
Grace: 150 + 90 = 240 (she had 90 more badges before)
Joyce: 180 - 90 = 90 (she had 90 fewer badges before)

First transfer: Eunice gave 2/5 of her badges to Grace.

She had 120 badges after she gave 2/5 to Grace, so 120 is 3/5 of her badges before the transfer.
She had 120 * 5 / 3 = 200 badges before the transfer, and she gave 80 badges to Grace.

Before Eunice gave some of her badges to Grace, the girls had

Eunice: 120 + 80 = 200 (she had 80 more badges before)
Grace: 240 - 80 = 160 (she had 80 fewer badges before)
Joyce: 90 (unchanged)

Answer: Eunice had 200 badges at first.

[ozora]

Question:

Catherine had some money at first. She gave 1/4 of her money to
Anne. As a result, Anne had thrice as much as before. Then, Anne
gave 1/2 of her money to Bernard. Bernard then had 1 1/2 times as
much money as before. Anne still had $129 left. How much money
did each child have at first?

Answer:

Anne

We work backwards for Anne. She had $129 at the end.
This was after giving half her money to Bernard. So, she gave $129 to Bernard.
Before giving $129 to Bernard, she had $129 + $129 = $258.
Anne tripled her money after getting 1/4 of Catherine's money.
So Anne had $258/3 = $86 at first.

Anne had $86 at first

Catherine

Anne tripled her money after getting 1/4 of Catherine's money.
As Anne had $86 at first, she received 2 x $86 = $172 from Catherine.
This was 1/4 of Catherine's money
So Catherine had $172 x 4 = $688 at first

Catherine had $172 x 4 = $688 at first

Bernard

Bernard received $129 from Anne, and had 1 1/2 times as much as before.
So the $129 was half what he had at first.
So Bernard had $129 x 2 = $258 at first.

Bernard had $129 x 2 = $258 at first

thanks
c

[peggy]

Please help with this -

Printer A can print 40 more worksheets than Printer B in one minute. In a printing job, Printer A took 10 minutes while Printer B took 15 minutes to print the same number of worksheets.
How many worksheets did each printer print ?

Thank you.

[nicnac]

Please help with this -

Printer A can print 40 more worksheets than Printer B in one minute. In a printing job, Printer A took 10 minutes while Printer B took 15 minutes to print the same number of worksheets.
How many worksheets did each printer print ?

Thank you.

According my DD, each printer printed 1200 worksheets.

40 * 10=400
400 * 5 = 80
80 * 15 = 1200

[wilburlim]

I need help for this question:

Amos, Ben and Charles shared the cost of a present. Amos and Ben paid 5/9 of the price of the present. Amos and Charles paid 2/3 of the price of the present. Amos paid $4. How much did the present cost?

Thank you!

[MathWithModels]

Amos, Ben and Charles shared the cost of a present. Amos and Ben paid 5/9 of the price of the present. Amos and Charles paid 2/3 of the price of the present. Amos paid $4. How much did the present cost?

Amos and Ben paid 5/9. This means Charlie paid 4/9.
Amos and Charlie paid 2/3. This means Ben paid 1/3.
Now, we can work out Amos' share. Charlie and Ben paid 4/9 + 1/3 = 7/9 altogether, so Amos share is 2/9. The present cost 9/2 x 4 = $18.

[EconsPhDTutor]

I need help for this question:

Amos, Ben and Charles shared the cost of a present. Amos and Ben paid 5/9 of the price of the present. Amos and Charles paid 2/3 of the price of the present. Amos paid $4. How much did the present cost?

Thank you!

Let A, B, and C be the amounts paid by each. Let X be the cost of the present.
We are told that

(1) A + B = (5/9) X,
(2) A + C = (2/3) X,
(3) A = $4.

Add (1) and (2) together to get

(4) 2A + B + C = (11/9) X.

But we know that

(5) A + B + C = X.

And so (4) minus (5) yields

(6) A = (2/9) X.

Together with (3), we have X = (9/2) × $4 = $18.


Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

www.EconsPhDTutor.com

If you found this answer helpful, then please help me out by spreading word of my services. I’m a new tutor in Singapore so I need some help getting word out! Thank you!

[wilburlim]

Thanks! One more question:

Aaron had 3/4 as many badges as Ben. Ben has 2/5 as many badges as Calvin. Aaron has 8 badges fewer than Ben. How many more badges does Calvin have than Ben?

[alfretztay]

Please help with this -

Printer A can print 40 more worksheets than Printer B in one minute. In a printing job, Printer A took 10 minutes while Printer B took 15 minutes to print the same number of worksheets.
How many worksheets did each printer print ?

Thank you.

According my DD, each printer printed 1200 worksheets.

40 * 10=400
400 * 5 = 80 (It should be 'divided by'. '1200' is the correct answer though.)
80 * 15 = 1200

[sushi88]

Thanks! One more question:

Aaron had 3/4 as many badges as Ben. Ben has 2/5 as many badges as Calvin. Aaron has 8 badges fewer than Ben. How many more badges does Calvin have than Ben?

A has 3u
B has 4u
u-> 8 (A has 8 fewer than B)
C's 2 parts -> 4u = B (because 2/5) so 3 parts -> 4u/2 x 3 = 6u
Calvin has 6u = 6 x 8 = 48 badges more than Ben