Adam and Rahmad shared some beads.if Adam gave one-third of his share to Rahmad,Rahmad would have 70 more than Adam.if Adam gave one-fifth of his share to rahmad,Rahmad would have 10 more Adam.how many beads does Adam have at first?
If Adam gave 1/3 of his beads to Rahmad, he'd have 2/3 left. so,
2a/3 + 70 = r + a/3
4a/5 + 10 = r + a/5
a/3 - r = -70
3a/5 - r = -10
4a/15 = 60
a = 225
220 = r+75
r = 145
so, if adam gives 1/3 to rahmad,
a has 150 and r has 220
if adam gives 1/5,
a has 180 and r has 190
225
Let's assume that Adam starts with x beads.
If Adam gave one-third of his share to Rahmad, Rahmad would have (x/3 + 70) beads. And Adam would have ((2/3)x - x/3) = (x/3) beads left.
If Adam gave one-fifth of his share to Rahmad, Rahmad would have (x/5 + 10) beads. And Adam would have ((4/5)x - x/5) = (4x/5) beads left.
Since we have two equations:
(x/3) = (x/5) + 10 => Multiply through by 15 to eliminate the denominators
5x = 3x + 150
2x = 150
x = 75
So, Adam starts with 75 beads.
To solve this problem, let's assume that Adam has "x" beads at first.
According to the problem, if Adam gave one-third of his share to Rahmad, Rahmad would have 70 more beads than Adam. This means that Rahmad would have x + (1/3)x = x + (1/3)x + 70 beads.
Simplifying this equation, we have x + (1/3)x + 70 = x + (4/3)x.
Next, let's consider the second scenario where Adam gives one-fifth of his share to Rahmad. In this case, Rahmad would have x + (1/5)x = x + (1/5)x + 10 beads.
Simplifying this equation, we have x + (1/5)x + 10 = x + (6/5)x.
Now, we have two equations:
1) x + (1/3)x + 70 = x + (4/3)x
2) x + (1/5)x + 10 = x + (6/5)x
To solve these equations, we can start by simplifying them:
1) (4/3)x + 70 = (4/3)x
2) (6/5)x + 10 = (6/5)x
In the first equation, we can subtract (4/3)x from both sides to cancel out the x term:
70 = 0
We have a contradiction, which means that there is no solution to the first equation. This means that the information given is inconsistent or incorrect.
Therefore, we cannot determine the initial number of beads Adam has based on the given information.