Kate had 5 times as many beads as Shelly at first. After, Kate gave away 648 beads and Shelly received 216 beads, they had the same number of beads in the end. How many beads did Kate have at first? Show your steps. Let a second grade student understand your steps.
Let's first assume that Shelly had x beads at first.
Since Kate had 5 times as many beads as Shelly at first, Kate had 5x beads.
After Kate gave away 648 beads, she had 5x - 648 beads remaining.
After Shelly received 216 beads, she had x + 216 beads.
Since they had the same number of beads in the end, we can set up the equation:
5x - 648 = x + 216
To isolate x, we subtract x from both sides:
4x - 648 = 216
Next, we add 648 to both sides:
4x = 864
Finally, we divide by 4 to solve for x:
x = 864 / 4 = 216
So, Shelly had 216 beads at first.
Since Kate had 5 times as many beads as Shelly at first, Kate had 5 * 216 = <<5*216=1080>>1080 beads at first.
Therefore, Kate had 1080 beads at first.