Nanyang Primary School 2007 PSLE Math Prelim
Question:
At a school carnival, there were 520 more girls than boys. 1/8 of the girls and 20% of the boys left the carnival. In the end, there were 488 more girls than boys.
(a) Did more girls or boys leave the carnival? How many more?
(b) How many children were there at the carnival in the end?

Once again, we have another challenging question and in order to solve it, we are required to do a bit of logical thinking.

To solve part a, we need to perform 3 case studies first:


Case 1 – Same number of girls & boys left the carnival

If there are an equal number of girls and boys leaving the carnival, the difference will still be the same, 520.

Case 2 – More boys left the carnival

If there are more boys than girls leaving the carnival, the difference will be greater than 520.

Case 3 – More girls left the carnival

If there are more girls than boys leaving the carnival, the difference will be smaller than 520.

(a) The question mentioned that after 1/8 of the girls and 20% of the boys left the carnival, there were 488 more girls than boys.

The difference given in this question is 488, which is smaller than the original difference of 520.

As such, can you identify which case study is closest to our question?

Yes, we should use case 3 (more girls left) because the new difference (488) is less than the original difference (520). Therefore, for above question, more girls left the carnival.

To calculate how many more girls than boys left the carnival, we need to analyze the 3 case studies again.

If the same number of boys and girls left the carnival, the difference would remain as 520.

Since there is a decrease in the final difference as compared to the original difference, therefore, using 520 - 488 = 32, we can justify that 32 more girls left the carnival.

This is illustrated in the diagram below:

(b) To solve part b and for illustration purposes, we assume 100% = 100u.

The strategy to solve part b is that you must be able to apply the technique of cutting the models separately.

To find 1/8 of the Girls model, you need to cut the 100u and 520 separately.

1/8 of 100u = 12.5u. If 12.5u left the carnival, 87.5u will remain.

1/8 of 520 = 65. If 65 girls left the carnival, 455 girls will remain.

Combining the 87.5u and 455 girls, the model of the Girls after 1/8 of them left will be as shown in the 'After' portion of the Girls model below.

To illustrate 20% of the Boys left the carnival, the 'After' portion of the Boys model shows 80u because 20u had left the carnival.

488 – 455 = 33

7.5u --> 33
Total units: 87.5u + 80u = 167.5u
167.5u --> 33/7.5 x 167.5/1 = 737
737 + 455 = 1192

From the model, we found that 7.5u = 488 - 455 = 33.

Therefore, 1u = 4.4

Since the total number of Boys and Girls = 87.5u + 80u +455 = 167.5u + 455, the total number of boys and girls at the carnival in the end is (167.5 x 4.4) + 455 = 737 + 455 = 1192.

Phew! That was tough, wasn't it?

Ok, I'll shall see you tomorrow, same time same channel :)

Norman Tien

http://www.pslemath.com