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Question
primary 5 | Maths
| Percentage
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Plz help solve this question with working. Thx in advance
40% = 4/10
1 - 4/10 = 6/10
Let Mina have 4 units at the end, Linda have 6 units, a total of 10 units.
Mina gave 3/7 of her stickers back to Linda in return.
1 - 3/7 = 4/7
So she had 4/7 of it left in the end, and that equals 4 units.
Looking at the numerator, notice that it is also 4.
Since 4/7 can be thought of as 4 units out of 7, Mina had 7 units before giving to Linda.
So she gave 3 units to Linda.
Stickers Linda had before given back by Mina = 6units - 3 units
= 3 units
Now before Mina gave back to Linda, Linda had given ⅓ of her stickers to Mina.
1 - ⅓ = ⅔
She had ⅔ of it left and that equals the 3 units.
So ⅓ = 3 units ÷ 2 = 1½ units.
So Linda gave 1½ units to Mina.
Linda's stickers at first
= 3 units + 1½ units
= 4½ units
Mina's stickers at first
= 7 units - 1½ units
= 5½ units
Difference at first
= 5½ units - 4½ units
= 1 unit
1 unit = 80 stickers
Mina gave 3 units to Linda.
3 units
= 80 stickers x 3
= 240 stickers
Since Linda gave ⅓ of her stickers to Mina at the start and Mina gave 3/7 back, to make things easier,
we make the denominator common.
3 x 7 = 21
Let Linda's stickers at first be 21 units.
Then Mina's stickers = 21 units + 80
Total = 42 units + 80
Linda gave ⅓ of her stickers, which
= ⅓ x 21 units (or 21 units ÷ 3)
= 7 units
Linda stickers after giving Mina
= 21 units - 7 unit s
= 14 units
Mina's stickers after receiving from Linda
= 21 units + 80 + 7 units
= 28 units + 80
Now, Mina gave 3/7 of her stickers back to Linda.
3/7 of it = 3/7 x (28 units + 80)
= 12 units + 34 2/7
(Don't worry about the fractions , it will be resolved later)
Linda's stickers in the end
= 14 units + 12 units + 34 2/7
= 26 units + 34 2/7
Mina's stickers in the end
= 28 units + 80 - 12 units - 34 2/7
= 16 units + 45 5/7
Difference
= 26 units + 34 2/7 - 16 units - 45 5/7
= 10 units - 11 3/7
Difference also = 60% - 40% = 20%
So 20% → 10 units - 11 3/7
Total = 100% → 5 x (10 units - 11 3/7)
= 50 units - 57 1/7
Now we know total also = 42 units + 80 ①
So 42 units + 80 = 50 units - 57 1/7
50 units - 57 1/7 = 42 units + 8 units - 57 1/7
Comparing this and the first equation,
We see that 8 units - 57 1/7 = 80
8 units = 80 + 57 1/7 = 137 1/7
1 unit = 137 1/7 ÷ 8 = 17 1/7
Mina gave 12 units + 34 2/7
= 12 x (17 1/7) + 34 2/7
= 205 5/7 + 34 2/7
= 240 stickers