Alisha had 114 more beads than Beena. After Alisha gave 96 beads to Beena, Beena had twice as many beads as Alisha. How many beads did Beena have at first?
original:
Beena ---- x
Alisha --- x+114
after give-away:
Beena ---- x+96
Alisha ---- x+114 - 96 = x + 18
x+96 = 2(x+18)
solve for x
To solve this problem, let's start by assigning variables to the unknown quantities.
Let's say "x" represents the number of beads Beena had at first.
According to the given information, Alisha had 114 more beads than Beena. So, Alisha had (x + 114) beads at first.
After Alisha gave 96 beads to Beena, Beena had twice as many beads as Alisha. This means Beena had (x + 96) beads.
Since Beena had twice as many beads as Alisha, we can set up the equation:
x + 96 = 2(x + 114)
Let's solve this equation step by step:
x + 96 = 2x + 228 (Distribute 2 to x and 114)
x - 2x = 228 - 96 (Subtract x from both sides)
- x = 132 (Combine like terms)
x = -132 (Divide by -1)
However, it is not possible to have a negative number of beads, so we can conclude that there was an error in the question or there is no solution for this problem.