This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Tuesday, September 20, 2011

### Catholic High School 2010 PSLE Math Prelim Paper 2 Q17

Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

Solution

At first

Daniel ---- 100% + 40%
Brandon ---- 100%
Calvin ---- 1 unit

After Daniel and Brandon each gave 20% of their stickers to Calvin…
Daniel ---- 100% + 40% - (28%)*
Brandon ---- 100% - (20%)**
Calvin ---- 1 unit + (28% + 20% of Dan and Bran --> 80% of 1 unit)#
Hence Calvin --- 1 unit + (48% of Dan and Bran --> 80% of 1 unit)

* 20% of 140% = 28%
** 20% of 100% = 20%
# Cal received 28% + 20% = 48% of (Dan + Bran), which is equal to 80% of Cal's original amount of 1 unit.

80% of 1 unit ---- 48% of total of Dan and Bran
0.8 unit ---- 48%
1 unit ---- 48% divided by 0.8 = 60%

In the end Calvin
1 unit + (48% from Dan and Bran)
= 60% + 48%
= 108%

(Daniel) more than (Calvin) in the end
(140% - 28%)## - (108%)
= 112% - 108%
= 4%
## Danile had 140% at first but gave 28% to Calvin

Daniel had 20 more stickers than Calvin in the end
4% ---- 20
1% ---- 20 divided by 4 = 5

Brandon at first
100% ---- 100 x 5 = 500
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://road-to-psle.blogspot.com/2011/09/catholic-high-school-2010-psle-math_20.html", "fetch_time": 1566584103000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2019-35/segments/1566027318952.90/warc/CC-MAIN-20190823172507-20190823194507-00326.warc.gz", "warc_record_offset": 160625101, "warc_record_length": 12070, "token_count": 471, "char_count": 1427, "score": 4.28125, "int_score": 4, "crawl": "CC-MAIN-2019-35", "snapshot_type": "latest", "language": "en", "language_score": 0.9363930821418762, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00047-of-00064.parquet"}