SOS mum:

Hi..ps help..Many tks and God Bless:)


(4) Mrs Tan spent 5/8 of her savings on a microwave oven and a refrigerator. 4/7 of the amount she spent was used to pay for the refrigerator. The refrigerator cost $280 more than the microwave oven. How much was her savings at first?

Model Method:

http://i60.tinypic.com/295pff9.jpg\">

From the model,

Difference in costs = 20u - 15u = 5u

$280 = 5u

1u = $280/5 = $56

Total savings = 7u * 8 = 7* $56 * 8 = $3136

SOS mum:

Hi..ps help..Many tks and God Bless:)


(4) Mrs Tan spent 5/8 of her savings on a microwave oven and a refrigerator. 4/7 of the amount she spent was used to pay for the refrigerator. The refrigerator cost $280 more than the microwave oven. How much was her savings at first?

Fraction multiplication method:

Let 'Savings' represent the total money saved by Mrs. Tan.

Total amount Mrs. Tan spent for fridge and oven = 5/8 * Savings

Fraction of money spent on fridge\t=\t4/7 * Total amount spent

Cost of Fridge\t=\t4/7 * 5/8 * Savings

Fraction of money spent on oven\t=\t3/7 * Total amount spent

Cost of Oven\t=\t3/7 * 5/8 * Savings
\t\t
Difference in costs\t=\t(4/7 * 5/8 * Savings) - (3/7 * 5/8 * Savings)

Difference in costs\t=\t1/7 * 5/8 * Savings
\t\t
$280\t=\t1/7 * 5/8 * Savings

Therefore, (after moving unknown term to left side),

Savings\t=\t($280 * 7 * 8)/5 \t=\t$3136
\t\t
Mrs Tan's savings at first was $3136.

2R-Mummy:

Pls help :

There were 50 more carrot cakes than yam cakes on sale in a cafe. After selling three times as many carrot cakes as yam cakes, there were 14 more yam cakes than carrot cakes left. How many carrot cakes did the cafe sell? :?:

SOLUTION:
http://i58.tinypic.com/e9smms.jpg\">

From the after model diagram:
We can see that,
3u -1u = 50+14 = 64
2u = 64
1u = 32
Total no. of carrot cakes sold = 3u = 3*32 = 96

PollutedS:

Hi all! Please help with these questions. Thanks!


1) The marked price of a television set is $715. At this price, the shopkeeper can make a profit of 30% on the cost price with each television set sold. If he allows a discount of 10% off the marked price for cash payment, calculate his actual percentage profit.

2) Start with $20. What is the resulting amount if decrease by 100% and then decrease by a further 100%?

Solution to Q1:

130% of cost price = $715
100% of cost price = 100*$715/130 = $550

Therefore cost price of TV set is $550

10% of $715 = $71.50
New sale price after 10% discount = $715-$71.50=$643.50

% profit from new sale price = (New sale price - cost price)/cost price*100
=(643.50-550)/550*100
=17%

For Question 2, answer will be -$20

patntee:

My take on this


http://i58.tinypic.com/302patd.jpg\">

laughingcat:

Need help in this. Don't know how to draw the modelling.

James had 1250 handphones and ipad in his shop. After selling 560 handphones and buying 240 ipads, he had the same number of handphones and ipads. How many ipad did James have at first?

Solution 1:
We first draw a model diagram to show the end result after selling 560 handphones and buying 240 ipads. Note both quantities are equal.

Then we draw the model diagram to show the quantity of each object at first (before the selling and buying).

We add a small rectangle (shaded) to the handphones to show a bigger quantity before 560 was sold. We remove a smaller rectangle (dotted and shaded) to show a lesser quantity before buying 240 more.

http://i62.tinypic.com/16ae24j.jpg\">

From the 2nd model diagram we have,
2u + 240 + 560 = 1250
2u = 1250 - 240 - 560 = 450
1u = 450/2 = 225
Answer: James had 225 iPads at first.

OliverNg:

hi i'm oliver, i'm new here. i need help for my math homework:


q1) Simon and Peter had a total of 900 cards. Simon gave 1/5 of his cards to Peter. Peter then gave 1/4 of his cards to Simon. In the end, each of them had the same number of cards. How many cards did Simon have at first?

Solution with Model Diagram:

We can draw model diagrams to trace the transfers in the reverse order as shown below.

The 1st model shows the situation in the end where each boy has same number of cards.
The 2nd model shows the situation before Peter gave Simon 1/4th of his cards.
The 3rd model shows the situation before Simon gave Peter 1/5th of his cards

http://i60.tinypic.com/r1d11f.jpg\">

Solution:

From the 3rd model diagram it is clear that:
No. of cards Simon had at first (beginning) = 5 units
No. of cards Peter had at first (beginning) = 7 units
Total units = 5+7=12
Each unit = 900/12=75
Therefore no. of cards Simon had at first = 5*75=375

Dragon Flame:

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.

+\tx\t-\ty\t=\t240\t-----------EQUATION 1
-\tx\t+\t5y\t=\t220\t-----------EQUATION 2
\t\t\t4y\t=\t460\t

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

Sruthi:

http://i57.tinypic.com/2ivhgxt.jpg\"> please let me know if thd working done is correct.is there any other alternative methods we can use to solve this problem

Alternate Method:

At First:
Let
Total salary = 100 units
Mr. Lin saves 30% of his salary
At first Savings = 30/100*100 units = 30 units

After Rise in Salary:
10% rise in salary means,
Total salary = 100 units + 10/100*100 units = 110 units
Mr. Lin still saves 30% of his new salary
In the end Savings = 30/100*110 units = 33 units

Difference in savings = 33 units - 30 units = 3 units.

It is given that,
Increase in savings after salary raise = $189
Therefore 3 units = $189
1 unit = $189/3 = $63

Salary at first = 100 units
Actual Salary = 100 * $63 = $6300

sharon.leemc:

Hi.. I need some help in guiding my dd in her math. She doesn't understand the concept of finding the greatest and smallest possible value be it round to the nearest ten or nearest hundred.

How do I guide her on this? Been very worrying for her..

Pls share with me if you do have any method in teaching her .

Thank you.

Hi Sharon,

I am assuming your DD knows the basic rules for rounding off numbers to nearest ten or nearest hundred.

Let us first tackle rounding off to nearest ten:

The only way for her to recognize that there are 10 values (numbers) that can be rounded off to the same ten and thereby understand that in this set of values, there is a greatest and a smallest possible value, let her make a table as shown below and fill it up by following the rules of rounding.

Then let her mark each set of ten values that round off to the same ten. I have shown each such set in different colour.

Then ask her to spot the greatest and the smallest value in the set.

If she practices this several times, she will get confident I am sure.

Hope this works.
http://i59.tinypic.com/2mr9oo1.jpg\">

COOKIE64:

SShufen bought some strawberries from the supermarket. After using 4/7 of it to make a strawberry cake , she bought another 36 strawberries and baked another cake exactly like the first. 3/7 of the remaining strawberries were jues to make jam. 16 strawberries were left,


A)!How many strawberries were used to make jam?
B) how many strawberries did she have at first?

Detailed Answer:
http://i62.tinypic.com/68bggz.jpg\">

From the model diagram,

Each small division in the right is 1 unit.

4u=16
1u=4

No. used for jam = 3u = 12

No. from 36 additional strawberries used for cake 2 = Total extra bought - no. used in jam - no. left in end
No. from 36 additional strawberries used for cake 2 = 36 -12 -16=8

Note that there were 3/7 of original total strawberries left after she baked Cake1. To bake Cake2 she needs to use same amount of strawberries as in Cake1 which is 4/7 of original strawberries.

This means that the 8 strawberries derived above must be equal to 1/7 of original strawberries since she was left with 3/7 after baking Cake1 and needs 4/7 to bake Cake2. (4/7 - 3/7 = 1/7)

Therefore,
1/7 of original strawberries = 8

Total original strawberries=7x8=56