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 By: Elaine2003 (offline)  Saturday, August 17 2013 @ 11:37 PM CDT (Read 1421 times)
Elaine2003

Q1. The number of pupils who passed the English test was 3/5 of those who failed the English test. The number of pupils who failed the Math test was 4/7 of those who had failed the English test. 225 more pupils failed the English test than Math test. How many pupils passed their English test?

Q2. Tim and Vicky had 100 toy cars altogether. After Tim had lost 25 of his toy cars and Vicky has lost 1/8 of his toy cars, they have the same number of toy cars left. How many toy cars did they have left??

Newbie

Registered: 08/21/12
Posts: 2

 By: echeewh (offline)  Sunday, August 18 2013 @ 01:06 AM CDT
echeewh

Hey Elaine,

Following are my worked solutions:

Q1.

Find the common denominator (multiple) of 5,7 that represents the number of units of pupils who failed English test. And this is 35 (FE).

PE = (3/5) = (21/35)
FM = (4/7) = (20/35)

Given that 225 more pupils failed the English test (FE) than Math test (FM), we have ...

FE - FM = 225
35u - 20u = 225
15u --> 225
1u --> 15

PE = 21u --> 21 × 15 = 315

==========

Q2.

Use <work backwards> method with model,

<After>

T |--------------------|
V |--------------------|

<process>

T: -25
V: -(1/8)V

After V lost (1/8) of his toycars, V will have (7/8) left. So in V's model <before>, the equal portion contains the 7 equal units (u) as shown. Likewise, in T's model <before>, its equal portion will also make up the 7u as V.

Hence V's model <before> is 8u as shown below and T's model <before> increases by 25.

<Before>

T |--|--|--|--|--|--|--|<-25->
V |--|--|--|--|--|--|--|--|

Given that T and V had 100 toy cars altogether at first,

T + V = 100
(7u + 25) + 8u = 100
15u = 100 - 25 = 75
1u --> 75 ÷ 15 = 5

Total (left) = 14u
14u --> 14 × 5 = 70

=========

Trust this helps.

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: Elaine2003 (offline)  Sunday, August 18 2013 @ 07:40 AM CDT
Elaine2003

Edward

Thanks alot for your explaination! It really help alot.

Cheers
Elaine

Newbie

Registered: 08/21/12
Posts: 2

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