Andre and Ryan like to share stickers. If Andre gives 10 stickers to Ryan, the ratio of Andre to Ryan's stickers will be 1: 8. If Andre gives 80 stickers to Ryan, their ratio will be 1: 10. How many stickers does Andre have?
(a-10)/(r+10) = 1/8
(a-80)/(r+80) = 1/10
8(a-10) = r+10
10(a-80) = r+80
8 a - 80 = r + 10
10 a - 800 = r + 80
---------------------------subtract
-2 a + 720 = -70
2 a = 790
a = 395
Let's assume that the number of stickers Andre has initially is "x".
According to the first statement, if Andre gives 10 stickers to Ryan, their ratio is 1:8.
This means that after giving the stickers, Andre is left with (x - 10) stickers and Ryan has (8 * 10) = 80 stickers.
According to the second statement, if Andre gives 80 stickers to Ryan, their ratio becomes 1:10.
This means that after giving the stickers, Andre is left with (x - 80) stickers and Ryan has (10 * 80) = 800 stickers.
We can set up the following equation based on the information above:
(x - 10) / 80 = (x - 80) / 800
To simplify this equation, we can cross-multiply:
800(x - 10) = 80(x - 80)
Expanding both sides of the equation:
800x - 8000 = 80x - 6400
Bringing the variables to one side:
800x - 80x = -6400 + 8000
Combining like terms:
720x = 1600
Dividing both sides by 720:
x = 1600 / 720
Calculating the value of x:
x = 2.22
Therefore, Andre initially has approximately 2.22 stickers.
To solve this problem, we can set up a proportion based on the given ratios.
Let's start by representing the number of stickers Andre initially has as "x".
According to the problem, when Andre gives 10 stickers to Ryan, the ratio of Andre's stickers to Ryan's stickers becomes 1:8.
So, after giving 10 stickers, Andre will have (x - 10) stickers, and Ryan will have (8/1) * 10 = 80 stickers.
Now, we can set up the first proportion:
(x - 10) / 80 = 1 / 8
To solve for x, we can cross-multiply:
8 * (x - 10) = 80 * 1
8x - 80 = 80
Adding 80 to both sides:
8x = 160
Dividing both sides by 8:
x = 20
So, Andre initially has 20 stickers.
Now, we can check if this answer is consistent with the second part of the problem.
According to the problem, when Andre gives 80 stickers to Ryan, the ratio of Andre's stickers to Ryan's stickers becomes 1:10.
So, after giving 80 stickers, Andre will have (x - 80) stickers, and Ryan will have (10/1) * 80 = 800 stickers.
Now, we can set up the second proportion:
(x - 80) / 800 = 1 / 10
To solve for x, we can cross-multiply:
10 * (x - 80) = 800 * 1
10x - 800 = 800
Adding 800 to both sides:
10x = 1600
Dividing both sides by 10:
x = 160
However, this value of x does not match our initial assumption that Andre initially had x = 20 stickers. Therefore, the given information is inconsistent, and we cannot determine the exact number of stickers Andre has.
Well, it seems like Andre has quite the sticker-giving habit! Let's solve this sticker mystery together.
We know that initially, when Andre gives 10 stickers to Ryan, the ratio between them becomes 1:8. So, if Andre gives away 10 stickers, he ends up with 1 part, while Ryan ends up with 8 parts.
Next, when Andre super-generously gives away 80 stickers, the ratio changes to 1:10. This means that Andre ends up with 1 part, and Ryan ends up with 10 parts.
Now, we need to find out how many stickers Andre started with. To do that, let's imagine that we can represent the initial number of stickers Andre had as "x."
When Andre gave away 10 stickers, he was left with x-10 stickers and could be represented by 1 part.
Then, when Andre gave away 80 stickers, he was left with x-90 stickers (because he already gave away 10) which is still represented by 1 part.
Since the ratio is the same, we can set up an equation:
(x - 10) / 1 = (x - 90) / 1
Cross multiply:
x - 10 = x - 90
Subtract x from both sides:
-10 = -90
Oops! It seems we've encountered a problem. The equation doesn't produce a valid solution. So either my calculations have gone bananas, or Andre has performed some sort of sticker magic trick!
I apologize for not being able to find a definite answer to your question. Maybe Andre is just a mysterious sticker wizard, after all!