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 By: Kuro (offline)  Monday, February 10 2014 @ 04:59 AM CST (Read 1401 times)
Kuro

Kindly help with the attached questions, thanks.

Junior

Registered: 12/31/06
Posts: 27

 By: echeewh (offline)  Monday, February 10 2014 @ 10:12 PM CST
echeewh

Hey <Kuro>

Only have time for 2 questions now. Follow up on the other 2 in due course.

My worked solutions for Q1 and Q2 are as follows:

***** - for alignment purpose

Q1.

Mr Yusoff had some stationery in his shop. 1/4 of them were pencils, 1/2 of the remainder were pens and the rest were pencil cases.
Below are the prices of the stationery.
1 Pencil \$0.40
1 Pen \$0.80
1 Pencil case \$1.20

He sold some pencils, pens and pencil cases in the ratio of 3:4: 5 and collected \$52.

Given that he sold 1/2 of the total number of pencils, how many pencil cases did Mr Yusoff have at first?

Solution:

Pencils(P) = 1/4 = 2/8
Pens(E) = (1/2) × (3/4) = 3/8
Pencil Cases (C) = 3/8

<Before>
P : E : C
2 : 3 : 3

Given 1/2 the total P were sold,
P: (1/2) × 2u = 1u

<Sold> ratio:
P : E : C
3 : 4 : 5

Given this <sold> ratio, we multiply the <before> ratio 3x as follows: (since the sold unit is 1 from the original <before> ratio)

<Before>
P : E : C
6 : 9 : 9

Using <number x value> method, we now have ...
(3u × 40) + (4u × 80) + (5u × 120) = 5200
120u + 320u + 600u = 5200
1040u -> 5200
1u -> 5

Pencil Cases (C) (at first) = 9u
9u -> 9 × 5 = 45

=========

Q2

Farmer Dan harvested some apples. He sold to Adam 3/4 of the apples and another 105 apples. He sold to Geraldine 3/4 of the remainder but took back 55 apples. Farmer Dan had 890 apples left.
(a) How many apples did Geraldine have after returning 55 apples to Farmer Dan?
(b) How many apples did Farmer Dan harvest?

Solution:

Apply <Branching> method, we have ...

Total(A) --|
************-- (1/4) - 105 (R)

*******************-- (3/4) - 55 (G)
(1/4) - 105 (R) --|
*******************-- (1/4) + 55 (R1) = 890

(1/4) + 55 = 890
(1/4) = 890 - 55 = 835
(3/4) = 3 × 835 = 2505

(a)
G = (3/4) - 55
= 2505- 55
= 2450

(b)
(1/4) - 105 (R) = 835 + 2505
(1/4) = 835 + 2505 + 105
= 3445

Total(A) = (4/4) = 4 × 3445 = 13780

========

Trust these help.

Do let me know again if there are further clarifications.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 625

 By: Kuro (offline)  Tuesday, February 11 2014 @ 12:12 AM CST
Kuro

Hi echeewh, thanks for your help.

Junior

Registered: 12/31/06
Posts: 27

 By: echeewh (offline)  Tuesday, February 11 2014 @ 10:27 PM CST
echeewh

Hey <kuro>

Following are the worked solutions to your remaining questions.

****** - for alignment purpose

Q3.

Observe the patterns in the sequence below. What is the missing algebraic expression in the box? Express your answer in terms of c.

|--------|--------| ***** |--------|--------| ***** |--------|--------|
| ** 5 *|** 4 **| ***** | 10b *|** b **| ***** |** 6 **|** ? **|
|--------|--------| ***** |--------|--------| ***** |--------|--------|
|* 5a *|** 2a *| ***** |* 40 *|** 2 **| ***** |** 2 **|** 5c *|
|--------|--------| ***** |--------|--------| ***** |--------|--------|

Solution

In the first Box, cross-multiply the numbers as follows:

5 × 2a = 10a
4 × 5a = 20a

Note: 2nd result is twice that of 1st result

in the second Box, do likewise as follows:

10b × 2 = 20b
b × 40 = 40b

Note: 2nd result is twice that of 1st result {same pattern as first Box}

in the last Box, do likewise as follows:

6 × 5c = 30c
? × 2 = 30c × 2 = 60c {2nd result twice that of 1st result}

Hence, ? = 30c

=========

Q4

Leon bought some terrapins and guppies for a total of \$\$96. He bought 3 times as many guppies as terrapins. He paid \$30 more for the terrapins than for the guppies. Each terrapin cost \$10.40 more than each guppy.

(a) How many terrapins did he buy?
(b) What was the cost of each guppy?

Solution

<Cost>
T |----------------------|
G |------------|<-30->

Given total amount for (T + G) is \$96,
amount (G) = (96 - 30) ÷ 2
= 66 ÷ 2 = 33

Amount (T) = 33 + 30 = 63

3u (G) = 33
1u (G) = 11

1u (T) = 63

Difference in cost between the same equal number of T and G is ...

1u (T) - 1u (G) = 63 - 11 = 52

Given that each terrapin (T) cost \$10.40 more than each guppy (G) ,

(a)
Number of T = 52 ÷ 10.40 = 5

(b)
5G = 11
1G = 11 ÷ 5 = \$2.20

=========

Trust these help.

Do let me know again if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 625

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