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 2 Maths questions
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By: Kuro (offline)  Thursday, June 27 2013 @ 11:00 AM CDT (Read 831 times)  
Kuro

Could some help solve the following 2 questions?

Q1.
3 children traded cards with one another.
At first, Eliza had more cards than Farhan and Michelle had 2 times as many cards as Farhan.
After Farhan bought another 33 cards, Michelle lost half of what she had and Eliza lost 14 Cards,
Farhan now had 6 'more cards than Eliza.
In the end, the children had a total of 150 cards. How many cards did each child have at first?
Ans: F=30 E=71 M=60

Q2.
Mrs Tan had some cupcakes. She packed 3/4 of the cupcakes into boxes.
Each box contained 4 cupcakes. She then packed 3/5 of the remaining cupcakes into containers of 6 cupcakes each.
In the end, she had 16 cupcakes left.
(a) Find the total number of boxes and containers she used to pack the cupcakes.
(b) If she sold each box of cupcakes for $10 and each container of cupcakes for $12,
how much did she earn after selling all these boxes and containers?
Ans: (a) 34 (b) $348

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By: echeewh (offline)  Thursday, June 27 2013 @ 09:35 PM CDT  
echeewh

Hi <kuro>,

Following are my worked solutions:

Q1.

*** - for alignment purpose

<before>
E |------------------------------|
F |-------|
M |-------|-------|

<process>
F: +33
M: -(1/2)M
E: -14

<After>

<---- : decrease

*********************** 14
********* <- 27 --><----------
E |-------------------|<-6->---| {E lost 14, but F had 6 more}
F |-------|<---- 33 ----->|
M |-------|-------|
********* <--------

Given that E,F,M had 150 cards at the end, we have ...

3u + 27 + 33 = 150
3u = 150 - 60 = 90
1u --> 30

At first:
E = 1u + 27 + 14 --> 30 + 41 = 71
F = 1u --> 30
M = 2u --> 2 × 30 = 60

===========

Q2

(3/4)total = (15/20)total (packed in boxes of 4)
(3/5) of remaining = (3/5) × (1/4) = (3/20)total (packed in containers of 6)

Hence, 2u of cupcakes were left.

2u --> 16
1u --> 8

(a)
Boxes of 4:
15u --> 15 × 8 = 120
120 ÷ 4 = 30 boxes

Containers of 6:
3u --> 3 × 8 = 24
24 ÷ 6 = 4 containers

hence, total number of boxes and containers used is 34.

(b)
Amount sold/earned:
30 boxes = 30 × 10 = $300
4 containers = 4 × 12 = $48

Total amount sold/earned is $348

==========

Trust this helps.

Do let me know again if there's further clarifications

Cheers,
Edward

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Registered: 04/21/11
Posts: 627

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