Things to note on 3 March 2015
(i) Math question 1
The tickets for a concert were sold as follows:
1 Adult ticket costs was $5
1 child ticket costs $2
There were twice as many children as adults. The amount of money collected was $1080. How many adults were there?
Method 1:
First, draw a model. 2 units for child and 5 units for adult. This is based on the price of each ticket.
Next, draw a model based on money collected for adults and child.
Draw 4 units for child and 5 units for adults. This means for each $4 we collect from 2 child, we collect $5 from 1 adult as there are twice as many children as adults.
Total number of units is 9.
1080 divided by 9 equals 120
This means that there are 120 adults.
Method 2:
For every 1 paying adult, there are 2 paying children as the question states that there are twice as many children as adults.
As such we look at them as a group.
Cost of tickets for 2 children = $2 X2 =$4
Cost of tckets for 2 children and 1 adult = $4 + $5 = $9
1080 divided by 9 equals 120.
As such there are 120 adults.
(ii) Math question 2
Ms Ong has a packet of sweets. If she gives 6 sweets to each of her pupils, she will have 2 sweets left. If she gives 7 sweets to each of her pupils. she will be short of 11 sweets.
(a) How many sweets are there in the packet?
(b) How many pupils does Miss Ong have?
(a) Using Listing method, the answer is 80 sweets.
38 sweets is unacceptable as the number of pupils (sequence) must remain the same for both the rows (multiples of 6 +2 and multiples of 7-11). This is because the number of pupils will not change in both given scenarios. You may compare this question with a similar Question 2 in Fan-math (Pg 15).
If you look at your listing table carefully, "38" falls until "6" and "7" pupils while "80" falls under 13 pupils for both rows. So the answer is "80".
This extra check is necessary as the sequence in this case, is the number of pupils which will not change in both given scenarios.
For listing questions involving systematic listing, pupils have to be careful in identifying what the seqence means and what the values (multiples) that they are calculating means before identifying the correct answers.
(b) Ms Ong has 13 pupils.
For Systematic Listing, please refer to Pg 14 of Fan-math.
