Bryan had some stickers. He gave 1/5 of his stickers to John and bought 4 new stickers. After that, he gave 1/3 of his remaining stickers to his brother and bought another 7 new stickers. In the end, Bryan had 55 stickers.
(a) How many stickers did Bryan give to his brother?
(b) How many stickers did Bryan have at first?
Let initial no. of stickers = N
Given to John = N/5
Remaining = N - N/5 = 4N/5
Bought 4 New
Now, no. of tickets = 4N/5 + 4
Given to brother = 1/3 of (4N/5 + 4)
= 4N/15 + 4/3
Remaining = (4N/5 + 4) - (4N/15 + 4/3)
= 4N/5 - 4N/15 + 4 - 4/3
= 8N/15 + 8/3
Bought 7 New
no. of stickers = 8N/15 + 8/3 + 7
= 8N/15 + 29/3
Now Bryan has 55
8N/15 + 29/3 = 55
8N/15 = 55 - 29/3 = 136/3
N = (136 * 15)/3 * 8 = 85
4N/15 + 4/3 = (4 * 85)/15 + 4/3
= (4 * 17)/3 + 4/3 = (68 + 4)/3
= 72/3 = 24
Let's solve this step-by-step:
(a) To find out how many stickers Bryan gave to his brother, we need to subtract the number of stickers he had at the end from the number of stickers he had before giving any to his brother.
Since Bryan had 55 stickers in the end, let's subtract the stickers he bought and gave to his brother:
55 - 7 = 48 (stickers remaining after buying 7 new stickers)
Next, we calculate the stickers Bryan gave to his brother:
1/3 * 48 = 16 (stickers given to Bryan's brother)
Therefore, Bryan gave 16 stickers to his brother.
(b) To find out how many stickers Bryan had at first, we need to work backward.
At the end, Bryan had 55 stickers. Before that, he bought 7 new stickers, so we subtract them:
55 + 7 = 62 (stickers Bryan had before buying the new stickers)
Before that, he gave 1/3 of his remaining stickers to his brother, so we reverse this operation as well:
62 * 3/2 = 93 (stickers Bryan had before giving any to his brother)
Before that, he bought 4 new stickers, so we subtract them:
93 + 4 = 97 (stickers Bryan had at the beginning)
Therefore, Bryan had 97 stickers at first.
To solve this problem, let's break it down step by step.
Let's assume the number of stickers Bryan had at first was x.
Step 1: Bryan gave 1/5 of his stickers to John.
This means Bryan gave (1/5)x stickers to John.
So, after giving away stickers to John, Bryan had (x - (1/5)x) stickers left.
Step 2: Bryan bought 4 new stickers.
So, the number of stickers Bryan had after buying new stickers is (x - (1/5)x) + 4.
Step 3: Bryan gave 1/3 of his remaining stickers to his brother.
This means Bryan gave (1/3) * [(x - (1/5)x) + 4] stickers to his brother.
After giving away stickers to his brother, Bryan had [(x - (1/5)x) + 4] - (1/3) * [(x - (1/5)x) + 4] stickers left.
Step 4: Bryan bought 7 more stickers.
So, the number of stickers Bryan had after buying more stickers is [(x - (1/5)x) + 4] - (1/3) * [(x - (1/5)x) + 4] + 7.
According to the problem, Bryan ended up with 55 stickers.
Therefore, we can set up the following equation:
[(x - (1/5)x) + 4] - (1/3) * [(x - (1/5)x) + 4] + 7 = 55
Simplifying the equation:
[(4/5)x + 4] - (1/3) * [(4/5)x + 4] + 7 = 55
Now, we can solve this equation to find the value of x.
(4/5)x + 4 - (4/15)x - (4/15)*4 + 7 = 55
(20/15)x - (16/15) + 7 = 55
(20/15)x + (104/15) = 55
(20/15)x = 55 - (104/15)
(20/15)x = 825/15 - 104/15
(20/15)x = 721/15
x = (721/15) * (15/20)
x = 721/20
So, the number of stickers Bryan had at first was 36.
(a) To find the number of stickers Bryan gave to his brother, we substitute x = 36 into the equation we derived earlier:
[(x - (1/5)x) + 4] - (1/3) * [(x - (1/5)x) + 4] + 7
[(36 - (1/5)*36) + 4] - (1/3) * [(36 - (1/5)*36) + 4] + 7
[36 - (36/5) + 4] - (1/3) * [36 - (36/5) + 4] + 7
[36 - 7.2 + 4] - (1/3) * [36 - 7.2 + 4] + 7
[32.8] - (1/3) * [32.8] + 7
32.8 - (1/3) * 32.8 + 7
32.8 - 10.933333333333333333333333334 + 7
28.866666666666666666666666666667
Therefore, Bryan gave approximately 28.87 stickers to his brother.
(b) From our calculations, we found that Bryan had 36 stickers at first.