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Need help on the above q.

Need help on the above q

Q1.The particpants of the quiz are divided equally into 2 groups.

in the first group, there are 20 more boys than girls.

in the second group, there are 12 more girls than boys.

45% of all participants are girls.

How many participants are boys?

 

q2. Suyin baked some pies. She gave 1/5 of them to her relatives and 30 of them to her friends. She was left with 2/3 of the pies. She packed these into 18 boxes . Some boxes contained 6 pies while the rest contained 12.

a) how many pies weee packed into 18 boxes?

b) how many boxes contained 6 pies?

 

Source: PSLE 2012 Maths

Answer

Q1) Frankly, all I did was summarising the data before I know what method to use and the results just “pops out” this way. You should deduce the same thing if you draw models of 2 different shapes for group 1 and 2 respectively.

                     Girls                Boys                      Diff

Group 1         u                    u+20

Group 2        p+12               p

Total          u+p+12         u+p+20                  8 —> 10%(diff of 55% boys and 45% girls)

                                                         Boys:   44 <— 55%                Corrected

0 Replies 1 Like ✔Accepted Answer

Q1. The participants of the quiz are divided equally into 2 groups. In the first group, there are 20 more boys than girls. In the second group, there are 12 more girls than boys. 45% of all participants are girls. How many participants are boys?

first group
boys ——- 1u + 20
girls ——- 1u

second group
boys ——- 1p
girls ——- 1p + 12

1u + 1p + 12 ——- 45% (total girls)
1u + 20 + 1p ——- 100% – 45% = 55% (total boys)
55% – 45% = 10% ——- 20 – 12 = 8
55% ——- (8/10) x 55 = 44

Ans : 44 boys.

Q2. Suyin baked some pies. She gave 1/5 of them to her relatives and 30 of them to her friends. She was left with 2/3 of the pies. She packed these into 18 boxes. Some boxes contained 6 pies while the rest contained 12. (a) How many pies were packed into 18 boxes? (b) How many boxes contained 6 pies?

(a)
total pies ——- 15u
(1/5) x 15u = 3u (relatives)
15u – 3u – 30 = 12u – 30 ——- (2/3) x 15u = 10u
12u – 10u = 2u ——- 30
1u ——- 30/2 = 15
10u ——- 150

(b)
18 x 6 = 108 (Assuming all 18 boxes contained 6 pies)
150 – 108 = 42 (pies in boxes of 12)
12 – 6 = 6
42/6 = 7 (boxes contained 12 pies)
18 – 7 = 11
or
18 x 12 = 216 (Assuming all 18 boxes contained 12 pies)
216 – 150 = 66
66/6 = 11

Ans : (a) 1566/6 = 110 pies; (b) 11 boxes.

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Thanks

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Welcome 

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Q2)

1 whole  —> take away 1/5 and 30      —-> left 2/3

1 whole  —> take away 3/15 and 30    —-> left 10/15 (LCM of 3 and 5 is 15)

                                                so  30 is 2/15 (balance fraction)

                                                                                       10/15 –> 30 x 5 = 150 pies (Ans a)

Part 2: Assumption method

If all 18 boxes contains 6 pies each –> 18×6=108 pcs

150-108=42 (big diff)

12-6 = 6 (small diff)

42/6 = 7 (must exchange 7 small boxes into big boxes)

18-7 = 11 small boxes of 6 pies (Ans b)

Check: 11 x 6 + 7 x 12 = 150 ok

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Thanks Sahm.

for q2)

is this method acceptable?

Give away =1u+30

left= 4u-30

1u+30 = 1p——eq1

4u-30 =2p ——eq2

as they indicated 2/3 are left. As such that I had the equation.

 make eq1 =eq2

eq1 x2 throughout

eq1;> 2u+60 =2p

4u-30=2u+60

4u-2u=60+30

2u=90

1u=45

4u-30=4×45-30

          =150

 

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Hi, yes it works as well. Just depends on which method your child prefers. I always suggest that child to try many methods. Can even encourage child to draw model. Since it is quite an easy model with 15 boxes to start with, should take the chance to practice too. So child feels more confident and energised to use different ways to enjoy Maths, like I still do. 🙂

Updated 26/5/17: Added model above. Quite straight-forward for most kids, I think.

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