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 By: shirley wee (offline)  Thursday, September 06 2012 @ 03:10 AM CDT (Read 883 times)
shirley wee

1) There were red and blue counters in a box. The number of red counters was twice the number of blue counters. Miss Phua gave 9 red counters and 7 blue counters to each pupil in her class. There were only 180 red counters left after all pupils got their share.
(a) How many pupils were there in Miss Phua's class?
(b) How many counters were in the box at first?

2) Andy mixes 4 kg of Grade A coffee powder with 5 kg of Grade B coffee powder. Grade B coffee powder costs \$4.50 per kg less than Grade A coffee powder. The total cost of the mixture is \$15.00 per kg.
(a) Find the cost of 9 kg of the mixture.
(b) Find the cost of 1 kg of Grade A coffee powder.

Chatty

Registered: 02/28/12
Posts: 68

 By: echeewh (offline)  Tuesday, October 23 2012 @ 09:06 PM CDT
echeewh

hi Shirley

Following pls find my worked solutions:

Q1.

Ratio / Proportion of counters given away:
R : B
9 : 7

Apply <work backwards> method, we have ...

<before>

R |---- 180 ----|<----- 9u ----->|
B |<---- 7u ----->|

Given that R = 2B, we have ...

180 + 9u --> 2 × 7u = 14u
14u - 9u --> 180
5u --> 180
1u --> 36

(a)
There were 36 pupils

(b)
Total counters (at first) = 180 + 16u --> 180 + (16 × 36)
= 180 + 576 = 756

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

Q2.

(a)
9 kg mixture = 9 x 15 = \$135

(b)
Let Grade A coffee powder be 1u per kg

Given that Grade B coffee powder costs \$4.50 per kg

less than Grade A coffee powder, we have ...

B = A - 4.50 = 1u - 4.50

Apply <Number x Value> method,

4u + 5(1u - 450) --> 13500
4u + 5u - 2250 --> 13500
9u --> 13500 + 2250 = 15750
1u --> 1750

Cost of 1 kg Grade A = \$17.50

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

Trust the above helps.

Do let me know again if these answers are different from your Answerkey or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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