Tutor MathsGuru: Ask me for your burning Maths questions!

[Brenda10]

Good afternoon Mathsguru and others,


I need help for the following P5 SA1 Q11. :?

Mrs. Sham had 4 times as many lollipops as chocolate bars. After giving 177 lollipops and 25 chocolate bars to her students, she had thrice as many chocolate bars as lollipops left. How many lollipops and chocolate bars did she have altogether at first?
(Given answer: 230)

Thank you for your help.

[Dharma]

starlight1968sg:

Dharma:

[quote=\"starlight1968sg\"]Hi mathsguru and others,

I need some help:
(1) P, T and V have 960 beads altogether. P gave some of her beads to T and the number of T's beads was doubled. Then T gave some of her beads to V and the number of V's beads was doubled. If the 3 girls had the same number of beads in the end, how many beads did P have at first.
(ans: 560)
How to solve it?


MTIA.

Since P, T and V had the same no. of beads at last ; each will have 960/3 = 320 beads at last

When T gave some of her beads to V and the number of V's beads was doubled
No. of beads T and V before T gave V some beads :
T : 320 + 160 = 480
V : 320 – 160 = 160

When P gave some of her beads to T and the number of T's beads was doubled.
No. of beads P and T before P gave T some beads :
T : 480 – 240 = 240
P : 320 + 240 = 560

Hi Dharma,
The number 320 is due to 960/3 = 320.
May I ask how to get the number 160?
MTIA.[/quote]We know that P, T and V had 320 at the end.

The strategy is to work backwards.

1. When T gave some of her beads to V and the number of V's beads was doubled

Before V gets some beads from T, V would have had ½ of the no. of beads he had at last.

So, 320 x ½ = 160 (V had 160 heads and received 160 beads from T, to have 320 beads at the end).

T on the other hand, must had (320 + 160) 480 beads at first before giving away 160 to V and up with 320 beads at last.

[Vanilla Cake]

starlight1968sg:

Dharma:

[quote=\"starlight1968sg\"]Hi mathsguru and others,

I need some help:
(1) P, T and V have 960 beads altogether. P gave some of her beads to T and the number of T's beads was doubled. Then T gave some of her beads to V and the number of V's beads was doubled. If the 3 girls had the same number of beads in the end, how many beads did P have at first.
(ans: 560)
How to solve it?

MTIA.

Since P, T and V had the same no. of beads at last ; each will have 960/3 = 320 beads at last

When T gave some of her beads to V and the number of V's beads was doubled
No. of beads T and V before T gave V some beads :
T : 320 + 160 = 480
V : 320 – 160 = 160

When P gave some of her beads to T and the number of T's beads was doubled.
No. of beads P and T before P gave T some beads :
T : 480 – 240 = 240
P : 320 + 240 = 560

Hi Dharma,
The number 320 is due to 960/3 = 320.
May I ask how to get the number 160?
MTIA.[/quote]Hi starlight1968sg,
Your question is from CHIJ 2009 P5 SA1 Paper 2 Q18. VC's younger sister had done this paper before and pls see whether you are able to understand her workings while waiting for Dharma's explanation.

Workings done by VC's P5 younger sister
Beginning
P-> 1 and 3/4u
T-> 3/4u
V-> 1/2u

Middle
P->u
T-> 1 and 1/2u
V-> 1/2u

End
P->u
T->u
V->u

3u->960
1 and 3/4u->560

Prema had 560 beads at first.

Submitted by VC's mum.

[Dharma]

Brenda10:

Good afternoon Mathsguru and others,


I need help for the following P5 SA1 Q11. :?

Mrs. Sham had 4 times as many lollipops as chocolate bars. After giving 177 lollipops and 25 chocolate bars to her students, she had thrice as many chocolate bars as lollipops left. How many lollipops and chocolate bars did she have altogether at first?
(Given answer: 230)

Thank you for your help.

Chocolates\t: 1u – 25 = 3p
Lollipops \t: 4u – 177 = 1p

12u – 531 = 1u - 25
11u = 531 – 25 = 506
1u = 46

Total no. of chocs & lollipops at first = 5u = 46 x 5 = 230

[Vanilla Cake]

Brenda10:

Mrs. Sham had 4 times as many lollipops as chocolate bars. After giving 177 lollipops and 25 chocolate bars to her students, she had thrice as many chocolate bars as lollipops left. How many lollipops and chocolate bars did she have altogether at first?

This is a 4-mark Q11 from CHIJ P5 2009 SA1 Maths paper. You need to wait for Mathsguru and others to provide model solutions. Here's what VC's P5 younger sister did to solve. Sorry, she didn't use models.

Before
L : C
4 : 1

After
L : C
1: 3

(4u-177)/(1u-25)=1/3
3(4u-177)=1(1u-25)
12u-531=1u-25
11u=506
5u=230

Mrs Sham had 230 lollipops and chocolate bars at first.

Submitted by VC's mum.

[Brenda10]

Thank you Dharma and Vanilla Cake for your kind help while waiting for mathsguru’s model. I really feel headache to go through all these SA1 papers to prepare for coming SA1 Exam.

[chrisho]

2 simple questions that need to find better way to explain to my son. d


1. James had twice as many marbles as Bob. After James lost 240 marbles, Bob had 3 times as many marbles as James. How many more marbles did James have Than Bob at first.

2.Peter is 8 years old and his mother is 30 years older than he. how old will Peter be when his mother is thrice his age?

TQ

[JayT]

Is it possible to solve the question below by models? Thanks, Mathsguru for setting up this thread!


In the begining, the ratio of Alan’s marbles to Kevin’s marbles was 3:4. After Alan bought another 9 marbles and Kevin lost 18 marbles, the ratio becomes 3:2. find the number of marbles Alan had at first.

[Dharma]

chrisho:

2 simple questions that need to find better way to explain to my son. d


1. James had twice as many marbles as Bob. After James lost 240 marbles, Bob had 3 times as many marbles as James. How many more marbles did James have Than Bob at first.


TQ

http://www.postimage.org/image.php?v=TsuDSr0

[Dharma]

chrisho:

2 simple questions that need to find better way to explain to my son. d


2.Peter is 8 years old and his mother is 30 years older than he. how old will Peter be when his mother is thrice his age?

TQ

Now
Peter : 8 yrs old
Mother : 8 + 30 = 38 yrs old

Difference in age = 38 – 8 = 30 years

THE DIFFERENCE IN AGE BETWEEN PETER AND HIS MOTHER IS ALWAYS 30 YEARS

When mother is thrice Peter’s age
Peter : 1u
Mother : 3u

Difference = 2u = 30 years
1u = 15 years

Peter will be 15 when his mum is thrice his age