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?
(a) Did more girls or boys leave the carnival? How many more?
(b) How many children were there at the carnival in the end?
After some boys and girls left, there were 488 more girls than boys.
But we know from the above model (marked in red) that
Girls remained at carnival ------- 7/8 unit + 455
Boys remained at carnival -------- 4/5 unit.
(Girls remained) – (Boys remained) = 488 more girls than boys
(7/8 unit + 455) – (4/5 unit) ---- 488
7/8 unit - 4/5 unit + 455 ---- 488
3/40 unit ----- 488 – 455
3/40 unit ----- 33
1 unit ---- 33 divided by 3/40
1 unit ---- 33 divided by 3/40
1 unit ---- 440 (the all important 1 unit)
Question (a) - Did more girls or boys leave the carnival? How many more?
Girls left carnival -------- 1/8 unit + 65
1/8 x 440 + 65 = 120 girls left.
Boys left carnival -------- 1/5 unit
1/5 x 440 = 88 boys left.
120 (girls) – 88 (boys) = 32 more girls than boys.
Answer for (a): 32 more girls than boys left the carnival.
Question (b) - How many children were there at the carnival in the end?
Girls remained at carnival ------- 7/8 unit + 455
Question (a) - Did more girls or boys leave the carnival? How many more?
Girls left carnival -------- 1/8 unit + 65
1/8 x 440 + 65 = 120 girls left.
Boys left carnival -------- 1/5 unit
1/5 x 440 = 88 boys left.
120 (girls) – 88 (boys) = 32 more girls than boys.
Answer for (a): 32 more girls than boys left the carnival.
Question (b) - How many children were there at the carnival in the end?
Girls remained at carnival ------- 7/8 unit + 455
7/8 x 440 + 455 = 840
Boys remained at carnival -------- 4/5 unit
4/5 x 440 = 352
Total remained ------ 840 (girls) + 352 (boys) = 1192 (children)
Answer for (b): There were 1192 children who remained at the carnival.
Boys remained at carnival -------- 4/5 unit
4/5 x 440 = 352
Total remained ------ 840 (girls) + 352 (boys) = 1192 (children)
Answer for (b): There were 1192 children who remained at the carnival.
1 comment:
Hi,
Not all difficult questions are good questions. What has this school accomplished? Nothing?
This is actually not a good question because the 'models' solution used is a thin mask for the algebra method. The unit is only a mask for variables like B.
The PSLE examiners should be interested in the method and not penalise the student for mistakes in calculation. If the student is able to draw and show the workings, I will still give 80% of the marks even if she/he goof up on the final steps.
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