Q&A - PSLE Math

[WenLee]

i couldn't solve this question after many attempts. :?


Jerry, Kathy and Luqman had a total savings of $450.60. The ratio of Kathy’s savings to Luqman’s savings was 3 : 5 at first. After Jerry and Kathy each gave 1/3 of their money to charity, the 3 children had $363.90 left. How much savings did Jerry have at first?

[Dharma]

leesf:

tianzhu:

Hi leesf


Look for Patterns is one of the heuristics in Primary Maths syllabus. You can observe a sequence such as pictures, shapes, letters, words, colours, or numbers. The given elements are in consecutive order.

Before doing PLMGS’s question, look at the following examples. Your kid may have done them before.

1) This pattern consists of four shapes (star, triangle,square,circle) that repeat in the same order. Find the 210th shape.

2) Next,look at a sequence of 4 letter word LOVE that repeats itself.

LOVELOVELOVELOVELOVELOVE
Find the 210th letter.

3) What day will it be 210 days from 28 February 2006?(A calendar showing Feb 2006 is showed in the question)

Use the same concept and apply to your question.

http://www.orlesson.org/orp/09Ma/2009-P6-Math-SA2-PLMGS.pdf
In this question, the first four elements are given. Please work out the next 4 or 5 elements by using the power functions of your calculator (approved model).Observe the pattern.The answer is 18.

Let your kid try it out first. Let me know if you need more clarification.

Hope this helps.

Best wishes

Hi Tianzhu,

Can you enlighten me on the above? Sorry, I still can't see the pattern from the above. Thanks

5 ^ 2 = 25
5 ^ 3 = 125
5 ^ 4 = 625
5 ^ 5 = 3125
5 ^ 6 = 15625
5 ^ 7 = 78125
5 ^ 8 = 390625
5 ^ 9 = 1853125
5 ^ 10 = 97655625

From 5 ^ 5 onwards, the last 4 digits will repeat itself in the following pattern: -
3125, 5625, 8125, 0625

If we take 3125 (which is 5 ^5) => 5 divide by 4 gives 1R1
We take the index and divide it by 4 and we get remainder as follows then we can determine the last 4 digits

5 divide by 4 => 1R1 => 3125
6 divide by 4 = > 1R2 => 5625
7 divide by 4 => 1 R3 => 8125
8 divide by 4 => 2 R0 => 0625

So, 5^210 => 210 divide by 4 => 52R2 => Remainder 2 => Last 4 digits = 5625

Sum of last 4 digits = 5 + 6 + 2 + 5 = 18

[tianzhu]

starlight1968sg:

My \"problem\" is when do we know we have to use equivalent ratios as in the case of 5:6 = 10:12 ?

Hi

The breakthrough for a student to solve this question is to recognise that the number of units remains the same for either case.

Whether from the MD or Units method, one can see that the difference for Elsie/Joyce in case1 and case 2 is 1 unit which is 4.

As this is a question on total unchanged concept, one needs to maintain the total number of units the same.

Therefore
1st case: 5:6 ----- 10:12 -------Total 22units
2nd case: 9:13 -----Total 22units

Best wishes

[tianzhu]

WenLee:

i couldn't solve this question after many attempts. :?


Jerry, Kathy and Luqman had a total savings of $450.60. The ratio of Kathy’s savings to Luqman’s savings was 3 : 5 at first. After Jerry and Kathy each gave 1/3 of their money to charity, the 3 children had $363.90 left. How much savings did Jerry have at first?

Hi WenLee

SA2 is around the corner and you may need the solution urgently.

A quick one,please draw a MD based on the description.Hope I've made no calculation errors.

Draw 1 bigger block to represent 1 unit for Jerry(1J) and 1 smaller block(1u) for Kathy and Luqman.

At first
3J ---Jerry
3u ----- Kathy
5u ----- Luqman

In the end
2J ------ Jerry
2u ------ Jerry
5u ------- Luqman

3J+3u+5u ------ 450.6 -----First
2J+2u+5u ------- 363.90 -----End

1J+1u ------ 86.70
3J+3u ------ 260.10
5u ------ 190.50
1u ------38.10

Therefore Jerry ----- 145.80

Best wishes

[WenLee]

[quote]\"At first

3J ---Jerry
9u ----- Kathy
15u ----- Luqman

In the end
2J ------ Jerry
6u ------ Jerry
15u ------- Luqman\"[/quote]Hi tianzhu

I am puzzled how u managed to get 9u and 15u for Kathy and Luqman? Can the working be started directly using 1J + 1U = $86.70, and work out Luqman's savings?

[yeodo]

Hi Parents


Can you please help with this question :

Luke spent 45% of his monthly income. For the month of July, his income was 30% less than August. His expenses for July was $648 less than his expenses for August. What was his income in August?

[tianzhu]

WenLee:

I am puzzled how u managed to get 9u and 15u for Kathy and Luqman? Can the working be started directly using 1J + 1U = $86.70, and work out Luqman's savings?

Hi

When I first read the question, I mistakenly read Lugman as giving 1/3 away. That's why I changed the 5 units into 15 units to allow for the 1/3 portion. In giving the solution I forgot to change the equivalent ratio back to 3:5.

Yes, you can use 1J+1U -----86.70 as Kathy is giving 1/3 away. You should get the same answer.

I am sorry for the inconvenience.Please refer to revised solution.

Best wishes

[WenLee]

[quote]Hi


When I first read the question, I mistakenly read Lugman as giving 1/3 away. That why I changed the 5 units into 15 units to allow for the 1/3 portion. In giving the solution I forgot to change the equivalent ratio back to 3:5.

Yes, you can use 1J+1U -----86.70 as Kathy is giving 1/3 away. You should get the same answer.

I am sorry for the inconvenience.Please refer to revised solution.

Best wishes[/quote]Hi tianzhu

Thank you v much for your help. Appreciated it very much.

[tianzhu]

WenLee:

Thank you v much for your help. Appreciated it very much.

Hi

You're welcome.

Best wishes

[yeodo]

Hi Parents


Please help with this question :

Luke spent 45% of his monthly income. For the month of July, his income was 30% less than August. His expenses for July was $648 less than his expenses for August. What was his income in August?