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

Answer: 500 stickers

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