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 By: shirley wee (offline)  Thursday, June 14 2012 @ 02:56 AM CDT (Read 847 times)
shirley wee

Hi! I am stuck with these mathematics questions again.

These are the questions:

4/5 of the children at a childcare centre were girls. After 14 girls and 1 boy had left the childcare centre, the ratio of the number of girls to the number of boys who remained at the childcare centre became 7 : 2. How many children were at the childcare centre at first?

Mrs Wong brought a bag of stickers to class. If she gives each pupil in her class 5 stickers each, she will have 20 stickers left. If she gives them 8 stickers each, she will need to buy another 88 stickers. How many stickers does Mrs Wong have?

Kimberly bought some sausages for a gathering. Her friends ate 3/4 of the sausages and 1/4 of a sausage. Kimberly then ate 3/4 of the remaining sausages and 1/4 of a sausage. If there were no sausages left, how many sausages did Kimberly buy?

Kenneth and Joanna were each given some money. If Kenneth spent half of the amount spent by Joanna, he would have \$2400 left. If Kenneth spent twice as much as Joanna, he would would still have \$900 left when Joanna had spent all her money.
a) How much money was given to Kenneth?
b) How much less money than Kenneth did Joanna have?

440 teachers and pupils participated in a tree planting event. Each teacher planted 2 trees and each group of 4 pupils planted 3 trees. If 455 trees were planted altogether during the event, how many pupils participated in the event?

Celestine has some twenty-cent coins and fifty-cent coins in the ratio 3 : 4. Given that all the coins add up to \$104, how many fifty-cent coins does Celestine have?

There was a total of 225 counters in Bags A, B, C, and D. 15 counters from Bag A were given away, 24 counters were added to Bag B, half of the counters in Bag C were sold and the number of counters in Bag D were doubled. As a result, there was an equal number of counters in each bag.
a) Find the number of counters in Bag B at first.
b) How many more counters were there in Bag C than Bag D at first.

At first, Wendy had twice as many balls as Fiona. After Wendy sold some of her balls, Fiona had twice as many balls as she had. Wendy sold each ball for \$6 and for every 4 ball that were sold, she received a bonus of \$5.
a) Given that Wendy received \$1218 in all from the sale of the balls, how many balls did she sell altogether?
b) How many balls did Wendy have at first?

Chatty

Registered: 02/28/12
Posts: 68

 By: echeewh (offline)  Thursday, June 14 2012 @ 09:44 PM CDT
echeewh

Hey Shirley ,
I feel there are just too many questions(8) posted as one. As it will take some time to complete all 8, I shall post worked solutions for the 1st 3 Questions as a start . Will provide remaining ones gradually.

Suggestion: Will be better if you can post your questions in separate posts ( perhaps limiting each post to 2 or 3 questions )

Here they are ...

Q1.

<Before>
G : B
4 : 1

<process>
14G, 1B left

<After>
7 : 2

Apply Cross-Multiply method, we have ...

(4u - 14) / 7 = (1u - 1) / 2
2 x (4u - 14) = 7 x (1u - 1)
8u - 28 = 7u - 7
8u - 7u --> 28 - 7
1u --> 21

Total children (at first) = 5u --> 5 x 21 = 105

=======================================

Q2.

<use Common Multiple method n list it out> -
1st IF: Add "whats left" to 5 as starting number; List out series of numbers by multiple (increment) of 5.
2nd IF: Minus "short of" (buy another 88) to 8 as starting number; List out series of numbers by multiple (increment) of 8.
Number: indicates number of pupils

Number: 1 .................... ......12 .... 21 ... 31 .... 36
5 + 20: 25 30 35 40 45 ....... 80 ... 125 ...175 ... 200
8 - 88: -80 -72 -64 -56 -48 ... 8 ... .80 .... 160 ... 200

Hence, number of stickers = 200

=========================================

Q3

<use Branching method or Model method>

(i)
Friends ate: 3/4 Total + 1/4 S (where S = sausage)
Remainder (R1): 1/4 Total - 1/4 S

(ii)
K ate: 3/4 R1 + 1/4 S
Remainder2 (R2): 1/4 R1 - 1/4 S

Given that no sausages were left, so R2 = 0.

Now we have in (ii) ...

1/4 R1 - 1/4 S = 0
1/4 R1 = 1/4 S
4/4 R1 = 1 S

in (i) we have ...
R1 = 1/4 Total - 1/4 S = 1 S
1/4 Total = 1 S + 1/4 S = 1 1/4 S
4/4 Total = 5 S

Hence, Kimberly bought 5 sausages.

===============================

Trust the above helps.

Do let me know if these do not agree with your answerkey ( if any).

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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