Q&A - PSLE Math

[Ice watch]

Mandy had $240 more than Serene. Mandy gave 60% of her money to Serene. Serene then gave 25% of her money to Mandy. As a result, Serene had $22 more than Mandy. How much did Serene have at first ?

Please help. Thank you.

[trytry]

Hi All,

Need your help to solve the question above.

Thanks & Regards
AT

Ratio.......Q..........R.....diff
...............3...........5......2

unshaded..Q..........R.....diff
.................7.........15......8

make diff the same
Ratio.......Q..........R.....diff
...............12.........20......8

unshaded..Q..........R.....diff
.................7.........15......8

common shaded part=20-15=5 or 12-7=5
5units------225
1unit-------45
15 units-----45x15=675 (unshaded R)

[Mathagog]

Mandy had $240 more than Serene. Mandy gave 60% of her money to Serene. Serene then gave 25% of her money to Mandy. As a result, Serene had $22 more than Mandy. How much did Serene have at first ?

Please help. Thank you.

Algebraic Solution Using Simultaneous Equations:

Let us assign variables to the money held by the two girls as below.
Mandy's amount at first = x
Serene's amount at first = y

From the first statement of the problem we have
x - y = 240 ----------------------------- EQUATION 1

After 1st transfer (Mandy gave Serene 0.6 of her money) we have,
Mandy's amount = 0.4x
Serene's amount = y + 0.6x

After 2nd transfer (Serene gave Mandy 0.25 of her money) we have
(A) Mandy's amount = 0.4x + 0.25(y + 0.6x)
(B) Serene's amount = 0.75(y + 0.6x)

Final result of these 2 transfers:
Serene's amount = Mandy's amount + 22

Now, we substitute the algebraic expressions for each amount from (A) and (B) into the final result to get,

0.75(y + 0.6x) = 0.4x + 0.25(y + 0.6x) + 22
0.75(y + 0.6x) - 0.25(y + 0.6x) = 0.4x + 22
0.5(y+0.6x) = 0.4x + 22
0.5y + 0.3x = 0.4x + 22
0.5y - 0.1x = 22

Multiply throughout by 10 to get,
5y - x = 220 ----------------------------- EQUATION 2

Solve the Simultaneous Equations by adding equation 1 and 2 so that variable x can be eliminated.

+ x - y = 240 -----------EQUATION 1
- x + 5y = 220 -----------EQUATION 2
4y = 460

Solve for y to get,
y = 460/4 = 115
Serene had $115 at first

[tianzhu]

The teachers in ABC Primary School are divided equally into 3 groups, X, Y and Z. The number of male teachers in Group X is equal to the number of female teachers in a Group Y. 1/4 of the school male teachers are in Group Z.

a) Find the ratio of the number of male teachers to the number of female teachers in the school.

b) If there are 45 female teachers in Group X and Y, how many male teachers are there in the school?

Hi Whitearies

Good afternoon

Hope this helps.

Best wishes.

[BigDevil]

Mandy had $240 more than Serene. Mandy gave 60% of her money to Serene. Serene then gave 25% of her money to Mandy. As a result, Serene had $22 more than Mandy. How much did Serene have at first ?

Please help. Thank you.

My take....

[Whitearies]

Amy and Tom each had some stamps. Firstly, Amy give 1/3 of her stamps to Tom. Secondly, Tom counted all his stamps and give 1/4 of them to Amy. Thirdly, Amy totalled her stamps and gave 1/5 of them to Tom. Finally, Amy had 32 stamps and Tom had 56 stamps. How many stamps did each of them have at first?

Thanks

[SAHMom]

Amy and Tom each had some stamps. Firstly, Amy give 1/3 of her stamps to Tom. Secondly, Tom counted all his stamps and give 1/4 of them to Amy. Thirdly, Amy totalled her stamps and gave 1/5 of them to Tom. Finally, Amy had 32 stamps and Tom had 56 stamps. How many stamps did each of them have at first?

Thanks

Working Backwards:
A 32; T 56
Amy left 4 parts (after giving 1 part out of 5 parts) and had 32 left.
1 part is 32/4=8
A is 32+8=40; T is 56-8=48

Tom left 3 units (after giving 1/4) and had 48 left.
1 unit is 48/3=16
so T is 48+16=64; A is 40-16=24

Amy left 2 sets (after giving 1/3) and had 24 left.
1 set is 24/2=12
so A is 24+12=36; T is 64-12=52

Check: every time, total is 88.

[tracywham]

Hi, need help for this question. My answer was differ from the given answer. Please advised.

In an hour, the number of chocolate boxes which had defective packing was 360 less than the number of boxes which were packed correctly.
If 60 more boxes were packed correctly in an hour, the number of boxes that are packed correctly would be 25 times the number of boxes with defective packing.
What is the total number of chocolate boxes packed in 1 hour?

[speedmaths.com]

Hi, need help for this question. My answer was differ from the given answer. Please advised.

In an hour, the number of chocolate boxes which had defective packing was 360 less than the number of boxes which were packed correctly.
If 60 more boxes were packed correctly in an hour, the number of boxes that are packed correctly would be 25 times the number of boxes with defective packing.
What is the total number of chocolate boxes packed in 1 hour?

Hi,

What is your answer?

What is the given answer?

[tracywham]

Given answer is 520.

I got 455