Edi bought some sweets.
Edi bought x sweets
On Thursday, he gave some sweets to his friends. The number of sweets given on
Thursday was 3/5 the number of sweets left.
He gave away y sweets, so he had x-y sweets left. So y = 3/5(x-y)
5y = 3(x-y)
5y = 3x-3y
8y = 3x
y = 3/8x
So since he gave away 3/8x sweets he had therefore had 5/8x left.
On Friday, he gave 130 sweets from the sweets left on Thursday to his neighbours.
So after Friday he had 5/8x - 130 sweets
The total number of sweets given over the 2 days
which was 3/8x + 130
was 4 more than 9/16 of the number of sweets Edi had at first.
3/8x + 130 = 9/16x + 4
126 = 9/16x - 3/8x
126 = 9/16x - 6/16x
126 = 3/16x
2016 = 3x
672 = x
(a) How many sweets did Edi buy?
Edi bought 672 sweets.
(b) How many sweets were left after the two days?
672 - (3/8x + 130) =
672 - 3/8x - 130 =
542 - 3/8(672) =
542 - 252 =
290
He had 290 sweets left over after the two days.
Let's check it in the words:
Edi bought some sweets.
He bought 672 sweets
On Thursday, he gave some sweets to his friends.
That was y = 3/8x or 3/8 of 672 or 252
The number of sweets given on Thursday was 3/5 the number of sweets left.
So he had 672-252 = 420 left and indeed the number given was 3/5 of 420 or 252.
On Friday, he gave 130 sweets from the sweets left on Thursday to his neighbours.
So after Friday, he had 420-130=290
The total number of sweets given over the 2 days was 4 more than 9/16 of the number of sweets Edi had at first.
The number given over the 2 days was 252+130=382
9/16 of 672 = 378. And, indeed, 382 is 4 more than 378.
Edwin
