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 By: Strawberry (offline)  Saturday, September 14 2013 @ 11:56 AM CDT (Read 1095 times)
Strawberry

1) The height of 4 boys are measured. If we add any 3 boys ' height and work out the average, we will have the following averages of 162 cm, 164 cm, 168 cm and 170 cm. Calculate the height of the tallest boy.

2) The height of 3 boys are measured. If we add any of the 2 boys' height and work out the average, we will have averages of 63cm, 69cm and 75 cm.

3) In a quiz for 100 pupils, the average score of the boys was 15 points higher than that of the girls. Given that the total points for the quiz was 7370 points and the average score of the boys was 80 points,find the number of boys who took part in the quiz.

4. Mrs Lim bought some bowls and plates in the ratio 3:2. She sold 3/4 of the plates and received \$1950. Given that the ratio of the cost of a plate to a bowl is 14:9 respectively. how much would she receive if she was to sell the remaining plates and bowls?

5) Lynette and Serene had some money in the ratio 3:5. They each spent part of their money on some books. The amount of money Serene spent was 11/2 times of what Lynette saved. The amount of money Lynette spent was 1.5 of what Serene saved. In the end, Lynette saved \$210 more than Serene. How much money did Serene save?

Regular Member

Registered: 01/31/09
Posts: 83

 By: echeewh (offline)  Monday, September 16 2013 @ 10:39 PM CDT
echeewh

hey <Strawberry>,

//updated 17/9, 15 30
My apologies for making a mistake to Q1. Here's the updated version. And many thanks to <AceAcademy> for pointing out the error.
//

Appreciate that you don't post so many questions on 1 thread as it may not be possible to answer all at one go.... . Perhaps an average of 2 will be just nice, and <Answerkey> is much appreciated for verification , if you do have. Thank you.

Btw, is there any question for Q2 ????

Anyway here are some of my worked solutions:

Q1.

Let the boys be A,B,C,D.

A + B + C = 162 × 3 = 486
A + B + D = 164 × 3 = 492
A + C + D = 168 × 3 = 504
B + C + D = 170 × 3 = 510

Sum of all equations above:
3A + 3B + 3C + 3D = 486 + 492 + 504 + 510
3(A + B + C + D) = 1992
(A + B + C + D) = 664 {total heights of 4 boys}

Height of tallest boy:
= 664 - 486
= 178 cm

==========

Q3.

Let number of boys (B ) = 1u
number of girls (G) = 100 - 1u

Total score (B ) = 80u
Total score (G) = 7370 - 80u

Given that average score of the boys was 15 points higher than that of the girls, we have ...

80 - [(7370 - 80u) / (100 - 1u)] = 15
[80(100 - 1u) - 7370 + 80u] / (100 - 1u) = 15
8000 - 80u - 7370 + 80u = 15(100 - 1u)
630 = 1500 - 15u
15u --> 1500 - 630 = 870
1u --> 870 ÷ 15 = 58

=========

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: aceacademy (offline)  Tuesday, September 17 2013 @ 12:45 AM CDT

Hi,

Q1's solution is incorrect. If the tallest boy is less than 60cm, the ave of any 3 boys' height can never be 162, 164, 168 and 170 cm.

The solution should read as follows:

Let the boys be A,B,C,D.

A + B + C = 162 x 3
A + B + D = 164 x 3
A + C + D = 168 x 3
B + C + D = 170 x 3

Sum of all equations above:
3A + 3B + 3C + 3D = (162 + 164 + 168 + 170) x 3
3(A + B + C + D) = 3 x 664
(A + B + C + D) = 664

Height of tallest boy:
= (664) - (162 x 3)
= 178 cm

Hope that helps.

Regular Member

Registered: 03/26/13
Posts: 88

 By: echeewh (offline)  Tuesday, September 17 2013 @ 03:39 PM CDT
echeewh

Hello <Strawberry>

Appreciate if you can verify Q4 , Q5 again. And , if possible, provide your <Answerkey> . Both don't work very well with the methods; hence the need to clarify.

Thank you,
Edward.

Active Member

Registered: 04/21/11
Posts: 627

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