The ratio of A's stickers to B's stickers was 3:4.
After A bought another 18 stickers and B lost 10 stickers, the ratio became 3:2. Find the number of stickers both of them had at first.
a/b = 3/4
(a+18)/(b-10) = 3/2
4a = 3b
2(a+18) = 3(b-10)
2a+36 = 4a - 30
2a = 66
a = 33
b = 44
check:
33/44 = 3/4
(33+18)/(44-10) = 51/34 = 3/2
Thank you, Steve!
aw, shucks <scuff><scuff>
To solve this problem, we can set up a system of equations to represent the given information.
Let's represent the number of stickers A had at first as "x", and the number of stickers B had at first as "y".
According to the first statement, the ratio of A's stickers to B's stickers was 3:4. This can be written as:
x/y = 3/4
After A bought another 18 stickers and B lost 10 stickers, the ratio became 3:2. This can be written as:
(x + 18)/(y - 10) = 3/2
We now have a system of two equations:
x/y = 3/4
(x + 18)/(y - 10) = 3/2
We can solve this system of equations to find the values of x and y.
First, we'll cross multiply the first equation:
4x = 3y
Now, let's simplify the second equation by cross multiplying and expanding:
2(x + 18) = 3(y - 10)
2x + 36 = 3y - 30
2x - 3y = -66
Next, we'll solve the resulting system of equations:
1. 4x = 3y
2. 2x - 3y = -66
To eliminate y, we can multiply equation 2 by 4 to match the coefficient of y:
8x - 12y = -264
Now, we can add equation 1 and equation 2 together:
(4x + 8x) + (3y - 12y) = 0 + (-264)
12x - 9y = -264
Simplifying this equation, we get:
4x - 3y = -88
Now, we have a new system of equations:
1. 4x - 3y = -88
2. 2x - 3y = -66
Subtracting equation 2 from equation 1 will eliminate y:
(4x - 3y) - (2x - 3y) = (-88) - (-66)
2x = -22
x = -11
Now, substitute the value of x back into equation 1:
4(-11) - 3y = -88
-44 - 3y = -88
-3y = -88 + 44
-3y = -44
y = (-44) / (-3)
y = 44/3
Thus, at first, A had -11 stickers and B had 44/3 stickers. However, it is not possible to have a negative number of stickers, so we can conclude that there is no solution to this problem.