KiasuAhMa:

Hi please answer the question below

It is p5 average

After a test, Peter and his friends calculated their average score.They found that if Peter got 14 more marks than what he did,they would have an average score of 88 marks. If Peter got 10 fewer marks than he did,their average score would become 85 marks. How many friends did Peter have?

Pls show workings too,thanks

Solution:

Let 'N' be the unknown number of children including Peter whose average is being calculated.

http://i57.tinypic.com/33mu0r9.jpg\">

From the model diagram we see that,

The total marks causing the change in average from 88 to 85 = 10+14=24.
Total marks of all children if Peter had got 14 more marks = 88xN
Total marks of all children if Peter had got 10 less marks = 85xN

Therefore,

Difference in totals,

88xN-85xN = 24
3xN = 24
N =24/3
N=8

Ans: Peter has 7 friends

leo_mums:

Jeremy had a total of 60 figurines of Smurf, Lego and Ironman. The ratio of the number of Smurf figurines to Lego figurines to Ironman figurines was 2:7:3. He bought another 30 figurines. As a result, the number of Smurf figurines was increased by 50% and the number of Lego figurines was increased by 20%. Find the percentage increase in the number of Ironman figurines.


*Is the answer 160% ?*

Solution:

At first,
Total figurines = 60
S:L:I = 2:7:3

If we represent ratio in units,

Total figurines = 12u
12u = 60
1u = 60/12=5

No. of Smurfs = 2u = 2x5=10
No. of Legos= 2u = 7x5=35
No. of Ironmans= 3u = 3x5=15

In end,
Total figurines = 60+30=90
Smurfs increased by 50% and Legos increased by 20%.

150% of Smurfs = 150/100x10 = 15
120% of Legos = 120/100x35 = 42

Rest are Ironmans.
No. of Ironmans in end = 90-15-42=33

% increase in Ironmans = (33-15)/15x100 = 120%
Ans: 120%

leo_mums:

At first, 30% of the beads in a bag were blue and the rest were yellow. There were 128 more yellow beads than blue beads. Some yellow beads were taken out, reducing its number by 25%. Find the ratio of the number of blue beads to the number of yellow beads in the end. Leave your answer in its simplest form.


*Is the answer 4:7 ?*

Solution:

At first,

Blue = 3u
Yellow = 7u

Difference = 4u
4u = 128
1u = 32

Total blue beads at first = 3u = 3x32=96
Total yellow beads at first = 7u = 7x32=224

In end,
Yellow beads reduced by 25% means they are now 75% of their number at first.
Yellow beads in end = 75/100x224=168

B:Y=96:168=12:21

leo_mums:

Blossom received more money than Bubbles from their father. 40% of Bubbles' money is $16 less than 25% of Blossom's money. If Blossom gives 35% of her money to Bubbles, Blossom will have $12 less than Bubbles.


a) How much money does Bubbles have?
b) Express the amount of money Blossom has more than Bubbles as a percentage. Round off your answer to 2 decimal places.

Solution using simultaneous equations:
Let
m = Blossoms money
n = Bubbles money.

From the second sentence of problem statement we can derive equation 1:

40/100 x n = (25/100 x m) - 16
After separating the knowns to one side and unknowns to the other we get,
1600 = 25m - 40n
Divide throughout by 5 to deal with smaller values,
320 = 5m - 8n ----------------------------> Eq1

From the last sentence of problem statement we can derive equation 2:

After giving 35% of Blossom's money,
65% of Blossoms money = Bubbles money + 35% of Blossoms money - $12
65/100 x m = n + 35/100 x m - 12
After separating the knowns to one side and unknowns to the other we get,
1200 = 100n - 30m
Divide throughout by 10 to deal with smaller values,
120 = 10n - 3m ----------------------------> Eq2

Now we eliminate one variable 'm' and solve for 'n'

320 = 5m - 8n ----------------->Multiply Eq1 throughout by 3
120 = 10n - 3m -------------->Multiply Eq2 throughout by 5

We get,
960 = 15m - 24n ----------------->Transformed Eq1
600 = 50n - 15m ----------------->Transformed Eq2
---------------------------

Add the two transformed equations to get,
1560 = 26n
n = 1560/26 = 60

a) Bubbles has $60

b) Substitute Bubbles value in equation 1 or 2 to solve for Blossoms money.
Blossom has $ 160

Money Blossom has more than Bubbles = $160 - $60 = $100
% money Blossom has more than Bubbles = $100/$60 x 100 = 166.67%

EC72:

40 pupils are required to make paper mobiles for an art project. Without a teacher's supervision, each boy can make 10 paper mobiles per hour while each girl can make 12 paper mobiles per hour. With a teacher's supervision, each pupil can make 2 more mobiles per hour. When the pupils are supervised for 2 hours, after which they are left unsupervised for 3 hours, a total of 2420 paper mobiles will be made. How many boys and girls are there?

Solution by simultaneous equation method:

Let,
B = total boys
G = total girls

Eqn1 : B+G=40

Total mobiles made by boys in some hours = Total boys x mobiles per boy x no. of hours

Total mobiles made by girls in some hours = Total girls x mobiles per girl x no. of hours

From the above formula we have,

Total mobiles made by both boys and girls in 2 hrs with supervision = Bx12x2 + Gx14x2
Total mobiles made by both boys and girls in 3 hrs without supervision = Bx10x3 + Gx12x3

Total mobiles made in 5 hrs = (Bx12x2 + Gx14x2) + (Bx10x3 + Gx12x3)
Total mobiles made in 5 hrs = 54B + 64G
2420 = 54B + 64G

Eqn2 :54B + 64G = 2420

To eliminate one variable, multiply Eqn1 with 54 and subtract this new eqn from Eqn 2.

54B + 64G = 2420
-(54B + 54G = 2160)
--------------------------
10G = 260

G = 260/10 = 26 Ans
B = 40-26 = 14 Ans

leo_mums:

The average cost of an iron, a fan and a vacuum cleaner is $30 more than the average cost of the iron and the fan. If the vacuum cleaner costs $125, find the total cost of the three items.

Model Diagram Method:

http://i59.tinypic.com/90okfr.jpg\">

The third model shows simple rearranging of the blocks to understand the correlation between the values given.

From the third diagram, we have,

$125 = 3x$30 + old Avg of Iron & Fan
Therefore,

Old Avg = $125 - $90 = $35

Total cost of iron, fan and vaccuum = 3x$30 + 3x$35 = $195

Ans: $195

EC72:

Nizal wanted to buy a piano but found that the amount of money he had was only 3/5 of the cost of the piano. He received $360 from each of his two sisters. The remaining 2/7 of the amount was paid for by his parents. How much money was paid by his parents?

Solution:

http://i57.tinypic.com/25ix9xg.jpg\">

From the model diagram,

4u = $720
1u = $180

Money lent by parents = 10u
10u = $1800

Ans: $1800

EC72:

A departmental store gave out gifts to commemorate its anniversary sale. Every 16th shopper who made a purchase was given a free notebook while every 20th shopper was given a free umbrella and every 40th shopper was given a free calculator. Karen was among the first 150 shoppers who made a purchase. In order for her to receive all the three gifts, how many shoppers had made purchases before Karen?

Solution:

For Karen to receive all the three gifts, she must be amongst the every 16th, 20th and 40th shopper.

This means she must be a common multiple of 16,20 and 40 which is 80.
So, if Karen is the 80th shopper, there must be 79 shoppers before her.

Ans: 79

The flower bracket for Yusof in the AFTER model diagram showing $576 should be all across the box (up to the end of the box).

Sorry for oversight.

vblurmum:

Halo, pls help me out with this question. If possible, pls show me the model drawing. Many many many thanks!!


Yusof had $576 more than Suhailah at first. After Yusof spent 7/10 of his money and Suhailah spent 13/20 of her money, Yusof had $37.40 more than Suhailah. How much did Suhailah have at first?

Solution:
http://i59.tinypic.com/2pyp0l5.jpg\">

1.We find Money Yusof is left with in end

Yusof Spent: 7/10 of his money
= 14/20 of Yusof's money
= 14/20 of (20 units + $576)
= 14 units + 14/20 x $576
= 14 units + $403.20
Money Left with Yusof = A in model + B in model
= 6 units + ($576 - $403.20)
= 6 units + $172.80

2. We find Money Suhailah is left with in end

Suhailah spent 13/20 of her money.
Money Left with Suhailah = 7 units

3. We calculate How much Suhailah had at first

After spending, Yusof was left with $ 37.40 more than Suhailah.
Therefore we have:
Yusof's money left = Suhailah's money left + $ 37.40
Substitute the values found above in (1) and (2) in this expression.
6 units + $172.80 = 7 units + $ 37.40
7 units - 6 units = $172.80 - $ 37.40 = $135.40
1 unit = $135.40
Suhailah's money at first = 20 units = 20 x $135.40 = $2708
ANS : $2708