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 By: drstevewu (offline)  Thursday, October 06 2016 @ 07:07 PM CDT (Read 1461 times)
drstevewu

1, Machine A took 80 minutes to produce some bottle caps. Machine B took 120 minutes to produce the same number of bottle caps. Machine A produced 5 more bottle caps per minute than Machine B,
(a) Both machines stared at 12 pm. What time will Machine A complete the job?
(b) How long would Machine A take to produce 3000 bottle caps?

2. There were 80 singers in a singing competition. The average score given for each singer is 58.5 points. The average score of the female singers was 64 and the average score for the male singers was 56 points. How many male singers participated in the competition?

Junior

Registered: 04/20/10
Posts: 31

 By: echeewh (offline)  Friday, October 07 2016 @ 08:48 AM CDT
echeewh

Hey <drstevewu>,

Appreciate it will be helpful if answer keys are also provided. Thank you.

Following are my worked solutions :

Q1.

(a)
80 minutes = 1 hr 20 min
1 hr 20 min from 12 pm is 1.20pm

(b)
Let the equal number of bottle caps be 1u.

<In 1 minute>
A: (1u / 80) bottle caps
B: (1u / 120) bottle caps

Given that Machine A produced 5 more bottle caps per minute than Machine B, we have ...

(1u / 80) - (1u / 120) = 5
(3u / 240) - (2u / 240) = 5
1u --> 5 × 240 = 1200

1200 --> 80 mins
3000 --> (80 / 1200) × 3000 = 200 mins ( 3 hrs 20 mins )

========

Q2.

Total score for 80 singers = 58.5 × 80 = 4680

Apply <Assumption> method, we have ...

Total score for 80 female singers = 64 × 80 = 5120

5120 - 4680 = 440
64 - 56 = 8
440 ÷ 8 = 55

There were 55 male singers.

=====

Trust these help.

Do let me know again if there are further clarifications or if these are different from the <Anskey>.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

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